In John 8:58 Yeshua says:
Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. (KJV)
If I'm not misunderstanding, and based on commentaries I've read, trinitarians believe this quote is god the son claiming to have existed from all eternity, even before Abraham.
Since the divine nature and human nature of god the son cannot be separated or divided, how did the human nature of god the son exist before Abraham?
Trinitarians do not teach that God the Son existed eternally in two natures, but that in the incarnation the divine nature assumed a human nature, and that these two cannot now be separated. This is clear in the Chalcedonian Definition, which distinguishes between the Godhead ("before the ages") and the Manhood ("the last days"):
before the ages begotten of the Father as to the Godhead, but in the last days, the Self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the Manhood
That the Son of God assumed (and did not have from eternity past) human nature is also clear in the Catechism of the Catholic Church:
Taking up St. John's expression, "The Word became flesh", The Church calls "Incarnation" the fact that the Son of God assumed a human nature in order to accomplish our salvation in it. (§461)
Similar points are made in Protestant catechisms, like the Westminster Shorter Catechism, Q22.
Turning now to treatments of John 8:58 in particular, we see Methodist Adam Clarke approvingly quoting Calmet (a Catholic), saying:
The following is a literal translation of Calmet's note on this passage: "I am from all eternity. I have existed before all ages. You consider in me only the person who speaks to you, and who has appeared to you within a particular time. But besides this human nature, which ye think ye know, there is in me a Divine and eternal nature. Both, united, subsist together in my person. Abraham knew how to distinguish them. He adored me as his God; and desired me as his Savior. He has seen me in my eternity, and he predicted my coming into the world." (source)
Similarly, Albert Barnes (Reformed) explains how John 8:58 should be understood to teach that only Christ's divine nature pre-existed the incarnation:
The objection of the Jews was that he was not 50 years old, and could not, therefore, have seen Abraham. Jesus replied to that that he existed before Abraham. As in his human nature he was not yet 50 years old, and could not, as a man, have existed before Abraham, this declaration must be referred to another nature; and the passage proves that, while he was a man, he was also endowed with another nature existing before Abraham, and to which he applied the term (familiar to the Jews as expressive of the existence of God) I AM; and this declaration corresponds to the affirmation of John (John 1:1), that he was in the beginning with God, and was God. (source)
Anything predicated of either of Christ's natures is predicated of the Person of the Son. Not only that nature. So that things proper to or only possible with either nature alone is still true of the Person.
Two examples:
The First and the Last (that is, a title for God) died. But only ini His (the Son's) human nature He can die. Yet what is predicated of His human nature is predicated of His Person. Revelation 1:17-18.
(The passage in question:) Jesus existed before Abraham because Jesus is not a nature (a 'thing') but a Person, even "the Word [who] was God..and was made flesh." John 1:1,14.
The First and the Last (that is, a title for God) died. . Moreover, it is correct in Chalcedonian Trinitarianism to say that God died in the flesh.
The question "how did the human nature of God the Son exist before Abraham?" does not follow from Jn 8:58 because Jesus said "I Am", not "my human nature exists". It is the divine Person Who eternally Is (God), and Who started to Be also human at some moment in 8-6 BC.
While the above is enough, I think I can enrich the coverage of this issue by relating it to the purely philosophical topic of the real distinction between essence and existence or act of being, as holding that real distinction (which afaik cannot be demonstrated from first principles) allows to provide, at the philosophical level, a description of the hypostatic union and an explanation of why Jesus' human nature is not a human person. The reasoning goes like this:
Christian doctrine of the Trinity states that each divine Person is the divine Essence. Those who also hold that in general there is a real distinction between essence and act of being must hold, per the doctrine of absolute divine simplicity, that the divine Essence is the Subsistent Act of Being, so that each divine Person is the Subsistent Act of Being. Therefore, the assumption of a human nature by a divine Person means that such human nature exists, from the moment of its creation, by the Subsistent Act of Being which that divine Person eternally Is.
In contrast, the position that the human nature of Jesus exists by its own contingent act of being gives rise to two serious problems:
A. Why would Jesus' human nature not be a human person?
B. Why did Jesus say "before Abraham came to be, I Am." (Jn 8:58) and not "before Abraham came to be, I Am in my divine nature."?
The only way to avoid these problems is to posit that in Jesus there is only one Act of Being, the eternal, Subsistent Act of Being of the Son. Therefore his human essence or nature does not exist by a created, contingent act of being, but by the Subsistent Act of Being of the Son. This case, in which a created essence does not exist by its own contingent act of being, shows that there is a real distinction between created essence and contingent existence.
