When was the term 'substitutionary atonement' first coined and what was the reason for the choice of the 2 words? The term 'substitutionary atonement' has been used within Trinitarian, Protestant, Reformed Baptist circles for some time, and it is those I wish to examine in this question.
But the word 'substitute' does not translate a Greek word found in scripture, nor does the term 'atonement'. The word 'atonement' is found once in the KJV, Romans 5:11, but it is a clear mis-translation of the word καταλλαγην, katallagen, in all other places rendered 'reconciliation'.
Both words are vague in meaning. Nor does 'substitute' or 'substitution' convey a concept that the apostolic epistles express, the emphasis of the doctrine of Christ being union with Christ (in his sufferings, in his death and in his resurrection) rather than some kind of 'exchange' (another word never found in Greek except μετηλλαξαν, metellazan, in Romans 1:26).
The word 'atonement' has a weak etymology and an ill-defined concept, its meaning a loose 'at-one' derivation and its application being a very general and overall term for the both the sufferings and death and resurrection of Christ that is never found in the greater precision of the apostolic writings.
What exactly is being conveyed by the term ? When was the expression first coined ? What error was being resisted by the introduction of this couplet ?
Again, I am looking for a response in regard to Trinitarian, Protestant, Reformed and Baptist usage of the terminology.

EDIT upon comment :
I believe that 'Christ died for our sins, according to the scriptures'. I believe that 'Christ gave his life a ransom for many'. I believe that 'He bare our sins in his own body on the tree'. I believe that 'he was made sin for us, who knew no sin'. But the scripture never uses the word 'substitute' to express that. I am questioning the terminology, not the doctrine of Christ.
Further explanatory EDIT :
My concern has always been the emphasis. If I have no relationship with Christ, if I am not in union with Him, if I know not his presence before my face when I pray, then the facts of his sufferings, death and resurrection are just that - historical facts.
The terms 'substitute' and 'exchange' are distant terms. But kinsman-redeemer, for example, (gaal in Hebrew) conveys a relationship that exists before the redemption takes place, (see the book of Ruth, on this). And one is chosen 'in Christ' (not apart from him) before the foundation of the world.
These are my concerns and the reason for my question.
It is hard to nail down a person or time that can be credited with the coining of the term substitutionary atonement.  The concept is not well attested in early extra-biblical writings although there are early variations/precursers such as Ransom theories (Origen) and vicarious atonement theories (Athanasius and Augustine).  It's first systematic exploration can probably be attributed to St. Anselm and even at this early date is has perhaps more to do with the penal aspect of atonement:

Theologian Marcus Borg (1942-2015) points out that the substitutionary understanding of Jesus’ death “was not central in the first thousand years of Christianity.” [1] Borg explains:
[The] first systematic articulation of the cross as “payment for sin”
happened just over nine hundred years ago in 1098 in St. Anselm’s
treatise Cur Deus Homo? [Why Did God Become Human?] Anselm’s purpose
was to provide a rational argument for the necessity of the
incarnation and death of Jesus.

Much like the absence of the exact words &quot;original sin&quot; or &quot;trinity&quot; from the biblical text, the idea of substitutionary atonement is integral to both what God, in Christ, has done for us and how this work was typified for us in the Levitical system of worship.
Substitute
a person or thing acting or serving in place of another.

a·tone·ment
reparation for a wrong or injury.
&quot;she wanted to make atonement for her husband's behavior&quot;

Propitiation -
hilastērion

Neuter of a derivative of G2433; an expiatory (place or thing), that is, (concretely) an atoning victim, or (specifically) the lid of the Ark (in the Temple): - mercyseat, propitiation.

Atonement -
kâphar,
kaw-far'

A primitive root; to cover (specifically with bitumen); figuratively to expiate or condone, to placate or cancel: - appease, make (an) atonement, cleanse, disannul, forgive, be merciful, pacify, pardon, to pitch, purge (away), put off, (make) reconcile (-liation).

Propitiation in the New Testament (Romans 3:24) and Atonement in the Old Testament (Leviticuas 16:10) both contain the nuance of expiation and I strongly believe that Leviticus chapter 16 demonstrates, in the sacrificed goat (lamb) and the released goat (lamb), the aspects of both substitution and atonement with  definite penal undertones, especially as regards the sin offering:

Lev 16:15  “Then he shall kill the goat of the sin offering that is for the people and bring its blood inside the veil and do with its blood as he did with the blood of the bull, sprinkling it over the mercy seat and in front of the mercy seat. Thus he shall make atonement for the Holy Place, because of the uncleannesses of the people of Israel and because of their transgressions, all their sins. And so he shall do for the tent of meeting, which dwells with them in the midst of their uncleannesses. - Leviticus 16:15-16 

The blood of the sin offering expiates or cleanses the Holy Place (which is within the veil) of the uncleanness of the people and also of the tent of meeting and the altar.  This opens the way for concord between God and His people.  The yearly ritual of Israel is a picture of the once for all entrance and cleansing of that which is behind and within the veil of human flesh so that the very Spirit of God may enter and dwell:

Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, by the new and living way that he opened for us through the curtain, that is, through his flesh, _ Hebrews 10:19-20

In fulfillment in Christ it is not a perpetual sacrifice (even the Levitical practice lasted for a year) but rather a sacrifice with perpetual effect (He entered once and sat down).  It is however, in type and fulfillment, both substitutionary and atoning.
Likewise the scapegoat:

“And when he has made an end of atoning for the Holy Place and the tent of meeting and the altar, he shall present the live goat. And Aaron shall lay both his hands on the head of the live goat, and confess over it all the iniquities of the people of Israel, and all their transgressions, all their sins. And he shall put them on the head of the goat and send it away into the wilderness by the hand of a man who is in readiness. The goat shall bear all their iniquities on itself to a remote area, and he shall let the goat go free in the wilderness. - Leviticus 16:20-22

This goat actually has ALL the iniquities AND the transgressions AND the sins of the people transferred from them onto it and it bears them away into the wilderness (outside the camp) so that the people may remain within the camp.  It is impossible to escape the notions of substitution and atonement/expiation here (v.10) as the scapegoat takes on and carries away that which is not it's own and cannot abide in proximity to God.  It is also difficult to avoid the penal aspect as well since the goat suffers the consequence of bearing iniquity (expulsion into the wilderness).
And so we have Jesus typified in two sacrificial animals.  One of them is killed in order to cleanse the place of God's dwelling and the implements of man's concord/worship with Him (the temple made without hands) and the other bears away into the wilderness all within man that separates him from God.  Both of these animals are substitutionary and provide atonement.