What reasons do Catholics have for believing Jesus is God? Through natural reason and personal experience, I have come to be convinced that many of the Catholic Church's teachings are good and accurate.  In addition, by reading Aristotle and Aquinas, I have come to see that there is a compelling natural argument for the existence of some sort of creator-God. I don't know that this argument convinces me, but I can at least comprehend it and think about it. 

That being said, there are many things in Catholicism that cannot be determined by natural reason alone -- the Trinity, the Immaculate Conception, etc. I find this sort of thing difficult to accept. Even more than difficult to accept, I find them difficult to think about. They are stories, they have value as stories, and there is certainly truth encoded in those stories. But are they factually true stories?  How could I know, and how do I even begin to think about that question? "God is one being with three persons" seems exactly as plausible to me as "God is one being with two persons".  

One particular issue I am looking at right now is the assertion of the divinity of Jesus.  This is an idea that is at the core of Christianity and at the core of Catholicism. And I find it to be difficult to choose to believe:  putting aside the mental gymnastics of the Trinity, the idea that a man who walked the earth was actually 100% God, the creator of everything, etc., is a very big assertion.  

So my question is this: what reason(s) might a non-Christian, non-Jew be given to be believe that Jesus is in fact God?  Historical examples of conversions and reasons for conversion are invited, as well as any other evidence or reasons.  I'm not looking for conclusive "proof" (a silly idea), but I am looking for reasons.  I am looking for ideas that parallel Aquinas's Five Ways or Chesteron's article Why I am A Catholic, but speak particularly about the assertion of the Divinity of Jesus. 

Given that I am currently trying to understand the teachings of the Catholic Faith in particular, I am primarily interested in answers that have a Catholic background. I mean no disrespect to Protestants, Orthodox, or any other Christians.
Right expectation of reason &amp; practical use of the Trinity
Aquinas's 5 ways is like a lens for reason to apprehend God as much as we are allowed to see with our reason alone.  The Chesterton's essay you mentioned is a great defense of Catholicism as a collective mind guarding the truth, which goes beyond reason to produce wisdom for believers, which he likened to a map of the maze, to navigate our way to the Truth in the midst of confusing half-truths and half-religions offered by the world.  If you trust Chesterton's presentation of Catholicism, isn't it reasonable to learn what Catholicism has to say on the divinity of Jesus, starting with her exegesis of the New Testament, her preservation and elucidation of the Patristic writings, and her deliberations and documents issued through the historical councils?  (The third section of my answer provides a rough outline)
From your question, it looks like your predicament is to make revelation fit to reason as a prerequisite to belief.  This is something that Chesterton himself has written about (specifically Chapter 2 &quot;The Maniac&quot; of his apologetic book Orthodoxy), and can result in madness because mad people try to fit things that are too big into a neat system (see the topic revisited here).  Chesterton values reason and logic, but he knows their limits.  St. Thomas Aquinas also knows the limits of reason although he expanded the field that can be known by reason so wide that even the modern philosophers shrunk in fear from it, cowardly narrowing the area that they say can be known by reason!  Therefore, not only modern philosophers try to fit God into their systems, they even narrow the capabilities of reason before they do that!  Double madness, in my opinion.
While I agree with you that &quot;there is compelling natural argument for the existence of creator-god&quot;, the same cannot be expected to discover the loving, just, and merciful character of God the Father, let alone the divinity of Jesus.  It has to come via revelation, but it can still be apprehended by reasonable faith.  We can use reason to assess the recorded testimonies of the revelation (NT writings plus the apostolic tradition) to re-present Jesus to us today, but accepting the claims of Jesus needs more than reason.  For instance, a lot of people who came across Jesus face to face and who witnessed His miracles while He was still on earth (i.e. revelation in person) did not accept Jesus's claims to be God, most notably some of the Pharisees.  Today, proper reading of the New Testament plus the testimony of the Holy Spirit in our hearts replace the face-to-face benefit that people in Jesus's own time had.
Catholicism, just like mainline Christian denominations, is very practical.  We are beings in need, God is the only supplier.  We don't need to completely understand the ingredients of spiritual food, we just eat and drink (as in communion).  Let God be God, and let human be human, who doesn't need to understand God completely to &quot;use&quot; Him.  We are like children who eat what our parents gave us when we were kids.
Similarly, we don't need to fit Trinity to reason, we just use the best definitions that the councils have produced.  I'm in software development; I don't need to understand how compilers and OS kernel works (although I can, since I have the training in Computer Science) but why bother?  I just read the documentation on how to use the compiler and how to call the kernel system call APIs.  It's a matter of trust (faith).  Do I trust the documentation to represent faithfully the compiler / OS Kernel?  Do I trust this compiler not to mess up my input?  Do I trust that this OS kernel has not had rootkit in it to turn my program into a booby trap that can extort people for money?  With good reason, I trust Microsoft Visual Studio 2019 and Microsoft Windows 10 Operating System.  (Some Linux die hard will think I'm mad :-) )
So Catholics trust Chesterton's map of the maze to find true north, and it's by using Catholic-produced Trinitarian understanding of God, Jesus, and the Holy Spirit.  From practical standpoint it's quite straightforward, and the data (the input) to the doctrine of Trinity is easy to understand (by reading the Bible carefully):

Jesus as prophet revealed God the Father to us, including His plan of the New Covenant.  He spent quality face to face time (about 3 years) with the 1st generation apostles teaching them many things, demonstrating miracles which only God the Father can produce as authentication.  His resurrection and subsequent appearance to the 1st generation apostles was the clincher and proof that He was a true prophet.
Jesus also claimed He was the only begotten Son of God the Father, making Him equal to God the Father.  John the Baptist (another prophet) was one of the witness when heaven opened and God the Father Himself testified that Jesus was His Son (see Matt 3:17).
When Jesus ascended back to the Heaven from where He came, He sent his Holy Spirit so He can still be with the believers entrusted to Him by the Father, but in a better way: closer to our hearts, and can be in many places at the same time (not limited to a single body while Jesus was still on earth).  Of course, because Holy Spirit is Jesus's spirit, and also God the Father's spirit, the Holy Spirit is also Divine.

Catholic Catechism paragraphs 1996-1999 is a good illustration how the Trinity is critical for our salvation:

1996 Our justification comes from the grace of God. Grace is favor, the free and undeserved help that God gives us to respond to his call to become children of God, adoptive sons, partakers of the divine nature and of eternal life.
1997 Grace is a participation in the life of God. It introduces us into the intimacy of Trinitarian life: by Baptism the Christian participates in the grace of Christ, the Head of his Body. As an &quot;adopted son&quot; he can henceforth call God &quot;Father,&quot; in union with the only Son. He receives the life of the Spirit who breathes charity into him and who forms the Church.
1998 This vocation to eternal life is supernatural. It depends entirely on God's gratuitous initiative, for he alone can reveal and give himself. It surpasses the power of human intellect and will, as that of every other creature.
1999 The grace of Christ is the gratuitous gift that God makes to us of his own life, infused by the Holy Spirit into our soul to heal it of sin and to sanctify it. It is the sanctifying or deifying grace received in Baptism. It is in us the source of the work of sanctification:

Therefore if any one is in Christ, he is a new creation; the old has passed away, behold, the new has come. All this is from God, who through Christ reconciled us to himself. [2 Cor 5:17-18]


And that's all there is to it to &quot;use&quot; Trinity in our faith life.  It's a matter of trust (similar to my trust in Microsoft products) which leads to practical actions: what do we do about it?  The Good News demands a response.  For what it's worth, in the next section I'll share my personal response, which is rather typical of many Christians, while trying to address why I believe Jesus is God, not just prophet / wise man.
A reason to believe Jesus is God (not just prophet / wise man)
You wrote:

I think this is both a really good answer and it also doesn't answer the thing I am trying to point at -- why? Why would someone who doesn't believe this choose to instead believe it?
I do not believe in Jesus or God in the way Christians do, no. That is why I'm asking the question. Catholicism has taught me a lot and I respect the Church's teachings, but this belief (among others) stands out as a difficult one to accept. I'm wondering why other people have chosen to believe it. I'm not asking for proof like one might prove 2+2=4 (it's not that sort of question); I'm asking for reasons.

If I may take your comment lightheartedly it sounds like you're a customer who would like the seller of the Christian doctrine to convince you into buying the product &quot;Jesus is God&quot; rather buying other seller's product &quot;Jesus is just a prophet&quot; or even another product &quot;Jesus is just a wise man&quot;.  And you want to hear customer testimonials why &quot;Jesus is God&quot; product works better for them so thereby giving you reasons to consider before buying.  Fair enough.  I respect that approach, and I would think Jesus Himself would have approved potential buyers to count the cost first before following Him.
I chose my screenname GratefulDisciple to reflect that I'm grateful to God that He has extended an invitation to me to be a &quot;proud owner&quot; of the product.  It's a badge of honor to be a disciple of Jesus, but as you can see in the &quot;count the cost&quot; link above, it's a product that &quot;owns you&quot; instead, so God (through Jesus &amp; the Holy Spirit) can &quot;fully manage&quot; your life and shepherd you into eternal life.
Why would you buy a product that owns you?  If you are in IT (like I do), you know it's the cloud era.  &quot;Managed product&quot; (aka software as a service) is the mantra.  You no longer own a software, not even a hardware.  It's like leasing a car.  You pay a monthly amount, no worries.  Accident?  Insurance takes care of it.  Mechanical issue?  Take it to the dealer.  Want a newer model?  Start a new lease period.  Your experience is better and better, and you are very productive, as long as you keep paying and you are okay with not owning the product.  Signing your life off to Jesus is the same way.  You give up control in exchange for total protection and total happiness (although not the kind of happiness that the world offers).
If Jesus were just a prophet or a wise man, I would not be getting total protection from Him.  A prophet is someone who says and/or shows something true about God, which may or may not be previously hidden.  A wise man is someone who teaches the way to success by explaining principles of life that are hard to obtain, the way master teacher trains an apprentice over many years.  Jesus was a prophet because He revealed the new covenant to us, i.e. the invitation to become children of God.  Jesus was also a wise man who taught that the way to eternal life (success) was by obeying the new covenant commandments, just like in the OT the way to God's blessing was by obeying the Torah.
But without Him being God as well, there was no new covenant and no total protection since being inducted into the new covenant involves buying into His identity as the Son of God and accepting all the consequences (like Jesus managing your life).  Or in Christian-speak, calling Jesus your Lord (a.k.a your #1 Boss) in exchange for a protection &quot;contract&quot; in which He is willing to die for you FIRSTLY to &quot;buy you out&quot; from the devil, SECONDLY to protect you from subsequent Satan's attacks who tries to get you back through temptations, and FINALLY to represent you as your attorney + bail-money on the Day of Judgment.  A mere prophet or wise man cannot give you that service.
Catholics' defense of the Divinity of Jesus across 2,000 years
The true nature of Jesus as 100% human and 100% God was clear to the 1st generation apostles and is still clear to us from the canonized 27 New Testament writings alone.  A good example of how the New Testament alone can show the divinity of Jesus can be read via an article by a well known Catholic apologist Tim Staples on how to answer Jehovah's Witness who does not believe Jesus is God and who does not believe in the authority other than the Bible text.
But in response to various heresies which developed in the first 400 years or so, the still united Catholic church had to clarify this teaching through several definitive councils, notably the Council of Nicaea (AD 325), the Council of Chalcedon (AD 451), and several church councils in between.  The article Jesus Christ, True God and True Man from Opus Dei, a Catholic spiritual formation organization, provides a good historical development of the doctrine.
In addition, early church fathers also wrote about the Divinity of Jesus, usually in their apologetic works.  Some quotes from individual church fathers can be read in a Catholic tract the Divinity of Christ.
St. Augustine of Hippo who wrote between AD 368 and AD 430, focused on combating the Manicheans, the Donatists, the Pelagians, and the Arians.  Only his writings against the Arians had to do with the true nature of Jesus, which is part of the larger effort outlined in the Opus Dei article above.  So his task was of refining rather than defending the Divinity of Jesus, which was already uncontested since he lived post-Nicaea.
St. Thomas of Aquinas who wrote between AD 1256 and AD 1273 was in another era altogether (High Middle Ages).  He no longer had to defend the Divinity of Jesus, but rather Christianity as a whole against Islam and also to reconcile the renaissance of Aristotelian philosophy (came via the Moslem scholars) with the Neoplatonic philosophy inherent in St. Augustine's theology, which made him famous as the most successful Catholic Doctor of the Church who was able to strike the right balance between Reason and Faith via his own adaptation of Aristotelian philosophy while maintaining orthodoxy in recasting Church Fathers teachings (including St. Augustine) in Aristotelian terms.
The Stanford Encyclopedia of Philosophy has a more formal treatment of the History of the Trinitarian Doctrines which includes quotes from St. Augustine and St. Thomas Aquinas but this is more of a philosophical analysis of the various conceptions of the Trinity rather than why Catholics believe Jesus is God.  That is an excellent resource to show what reason can do with the doctrine of Trinity, and complexity-wise, it's on par with Aquinas's 5 ways.  But does it help to accept the claim that Jesus is divine?  I don't think so.
Jumping to the past 100 years, the Divinity of Jesus was under fresh attack by liberal theologians of all stripes (Catholic / Protestant leanings), philosophers, and various projects undermining the reliability of the New Testament.  In defending the faith, Catholic and Protestant scholars often join forces, quoting each other in their scholarly books such as the 3 volume Jesus of Nazareth by Pope Benedict XVI (published AD 2007, 2011, 2012) and Jesus and the Victory of God by N.T. Wright (published AD 1996).  The Catholic church documents in this era were more of relevancy of Jesus to the Faithful such as

Jesus as the incarnation of Mercy (Dives in Misericordia, AD 1980)

Jesus as the incarnate love of God (Deus Caritas Est, AD 2005)


Of course I cannot leave out the Catholic Catechism which teaches Jesus as the Son of God in Chapter 2, Article 2.