Why did Christianity not follow Philo of Alexandria's definition of logos?

I'll focus on this question, "So why did the Christian view not follow this definition and instead make the leap to describing logos as part of God?"

It is because the logos/Word of God is identified as the second person of the Trinity.

John makes this connection explicit in the opening of his Gospel: "In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made. In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it... And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth" (John 1:1-5, 14).

Again, in Revelation, the rider on the white horse is called "Faithful and True" and, "He is clothed in a robe dipped in blood, and the name by which he is called is The Word of God" (Rev. 19:13).

The same Word through whom the Father spoke all things into existence (Genesis 1) came in the flesh to save his fallen creation (John 1) and is returning to complete the restoration of creation (Rev. 19).

The early Church Fathers also spoke of the Word/logos as being the Son of God, Jesus Christ, the Second Person of the Trinity.

For example, Athenagoras in chapter 10 of "Embassy for the Christians" says, "The Son of God is the Logos of the Father, in idea and operation. For all things were made after the pattern of Him and by Him - the Father and the Son being one. The Son is in the Father and the Father is in the Son, in oneness and power of Spirit. The Understanding and Reason of the Father is the Son of God" (http://www.ccel.org/ccel/schaff/anf02.v.ii.x.html).

Justin Martyr, in his first "Apology" written to the Roman emperor, also argues that the logos is the Son of God and draws comparisons with pagan myths as a point of connection with his Roman audience. His point being that this "logos" whom the pagans idolized is the very Son of God who came to restore his creation through his death and resurrection. See, for example, chapters 21 through 23, beginning at: http://www.ccel.org/ccel/schaff/anf01.viii.ii.xxi.html

Because that's Gnosticism.

In short, the early Christian Church had a fair amount of internal factional conflict over what their beliefs were and were not, and some of that made its way into the books of the New Testament. This is why you see statements saying things like that Jesus assumed fully the flesh of humanity, and wasn't just a spirit that made itself look human.

Most notably, they dealt with the Gnostics who believed in the sort of thing described in the OP, and who were thoroughly repudiated by the main line of the Christian Church.

If I can restate your question as follows:

Philo used the term Logos to mean an intermediary divine being. So why did Christianity not follow this definition and instead describes the logos as part of God?

Firstly, to say that the logos in Christianity is a “part of God” is an interesting choice of words:

In Greek philosophy, God has no parts (divine simplicity). Christian philosophy has adopted this principle.

In the first three centuries, Christian theologians did think of the Son as part of God. Remember, for example, the famous saying of Tertullian – “The Father is the entire substance, but the Son is a derivation and portion of the whole.”

In Eastern Orthodoxy, God is the Father only and the Son is the logos of the Father (the Word of God). The Son and the Spirit are like the two hands of God. Therefore, in Eastern Orthodoxy, we could say that the Son is part of God.

In the Athanasian Creed, the Trinity is God. The Son has been “begotten” by the Father but there is a very strong emphasis on the one-ness of God (the one-ness of the Trinity). I do not think we can speak of the Son as “part of God” in the Athanasian Creed. It does not present God as consisting of parts.

In popular Christianity, believers may understand the Son as part of God because of the formula - one Being but three Persons - perhaps not realizing that “Person” in the Trinity doctrine is not as we understand a person normally. In the traditional understanding of the Trinity, the Trinity has only one undivided substance and only one mind or will.

So, I would like to understand from what perspective you speak when you say that the Logos in Christianity is a part of God.

Secondly, I would like to propose that, in Philo, the logos is as least as much part of God as in Christianity. In Philo, the logos is:

• An “aspect of the divine” (Philo's view of God - Wikipedia);
• The "Creator's thoughts;” "Philo probably was the first philosopher who identified Plato's Ideas with Creator's thoughts. These thoughts make the contents of Logos" (Philo - Wikipedia) In this way, “the Logos of the living God” can be understood to be the mind or wisdom of God, as in Greek philosophy which Philo merged with Jewish exegesis of the Scriptures.
• "The first-born of God” - As in the NT, we can understand this to say that He came out of the being of God.
• The Universal substance on which all things depend. (Philo's view of God - Wikipedia)

While there are differences between Philo's understanding of the λόγος¹ and that of orthodox Christianity, there are also many similarities.

In fact, in On Dreams (De Somniis), I, §230, concerning the phrase «ἐγώ εἰμι ὁ θεὸς ὁ ὀφθείς σοι ἐν τόπῳ θεοῦ» (Gen. 31:13 LXX), that is, "I am the God who was seen by you in the place of God," Philo wrote, «καλεῖ δὲ θεὸν τὸν πρεσβύτατον αὐτοῦ νυνὶ λόγον», that is, "And what he now calls 'God' (θεὸν) is His most ancient word (λόγον)." We then see that even Philo was not immune to referring to the λόγος as God.

Footnotes

^{1 Why shouldn't we anticipate differences, especially since Philo was not a Christian?}