Why did the Apologists adopt Stoic Philosophy of the λόγος? The Greek word λόγος is a prevalent concept in the first century Greco-Roman world. It has many meanings like divine principle, reason, word and revelation. All of these views regards the λόγος as impersonal but Christians went beyond this age-old tradition and reinterpret the λόγος from personification to a real person subsisting.

God has reason, mind, will and emotion( Psalm 45:1 LXX).Hence, God is a person.The nature of God is eternal ( Romans 1:20).Ergo, God is an eternal person.

John the Apostle wrote that the λόγος is God by nature and hence, teaching us that the λόγος is a person because God's nature includes personality.

John 1:1 is clear that the λόγος is with God and is also God.The immediate context reveals how is the λόγος God by nature and this is by being the μονογενὴς of the Father (John 1:14,18).

God = Person ( the Father- John 1:14) 

λόγος =Person because God by nature ( the μονογενὴς in the Father's bosom - John 1:18)

But in the second century, the Logos Theology of the Greek and Latin Apologists began teaching that the λόγος is not an eternal person like what was taught in John 1:1 but rather, they adopted the Stoic terms of "logos endiathetos" ( Reason within) and "logos prophorikos" ( Reason expressed from the inside out) in order to teach that God is not an eternal Father and that the λόγος is not an eternal Son although they still teach that the Son is God and is of same nature with the Father.

Sources:

Against Praxeas Chapter 7 

Dialogue with Trypho Chapter 61

Now this is my question:

Why did the second century Apologists adopt the Stoic distinction of the "logos endiathetos" and the "logos prophorikos" to teach Christ's deity?
The 2nd century Apologists took advantage of Stoic Philosophy to advance the Gospel. 

The Greek word λόγος succinctly means something like word, message or reason "from the inside out."

The Apologists adopted the Stoic distinction of the λόγος for one purpose: evangelism.

The Apologists used the Stoic concept of the Logos as a means of arguing for Christianity to non-Jews. Since a Greek audience would accept this concept, their argument could concentrate on identifying this Logos with Jesus.

Logos endiathetos - The conceived Word.

One who is conceived does exists. 


  "My heart produced the most excellent Logos." ~ Psalm 45:1 (Septuagint)


Logos prophorikos - The nativity or birth of the Word.

One who is born existed priorly from the womb.


  "I have given birth to you in my womb before the star of the morning." ~ Psalm 110:3 ( Septuagint)


Note

The Apologists ( like Justin Martyr, Titan and Tertullian) had a good intention (i.e. soul winning) but they'd compromised and this is where they erred.It seems that if it were not their intention to lessen the deity of Christ, they did still come to that way which as history shows paved the way to Arianism. In other words, the Apologists obscured the doctrine of the divinity of Christ by Stoicism.Nevertheless, the Apologists weren't the only Christians in their day, there was their contemporaries like Irenaeus , Athenagoras, Gregory of Thaumaturgus, Novatian and Dionysius of Rome who all taught that the λόγος was the eternal Son.