This is an interesting question.  To be honest, I had never looked carefully at this verse.  It is an interesting statement by Jesus that he lives because of the Father.  Jesus makes a curious analogy here.  “Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me.”  The challenging part to understanding this analogy is that about himself he says two things, but about us he says one thing.  So what, exactly, is the analogy?   It can appear that Jesus is saying that if the Father had not given him life, then he would not live.  But we know from other passages that this is not what Jesus is saying, as we know that Jesus was with the Father from the beginning. (John 1:2)

To be honest, I am not entirely sure what Jesus is saying here.  Let me create my own paraphrase.  The life I give to you is given to you from the Father through me.  If you feed on me, then you will have eternal life, and that eternal life comes through me from the Father.    Another possible paraphrase is this.  I live (in the sense of occupying a human body) because the Father asked me to take on human flesh.  In the same way that the Father has asked me to take on human flesh and I have life in this body because of him, I am giving life to your mortal body as well.

Which is correct?  I am not sure.  What I am sure of is this–Jesus is not declaring that, like us, he is a created being.  I know this from John 8:58-59, John 1:1-2 and others.  A principal of biblical interpretation is that we interpret difficult passages (such as John 6:57) in light of more plain and clear passages (such as John 8:58-59 or John 1:1-2).  Therefore, although the two possible interpretations I am offering may seem not to be the most obvious interpretation of John 6:57, the interpretation that Jesus is telling us that he is a creation of the Father is clearly to be rejected under the assumption that all Scripture is inspired by God, which I strongly believe.

Sorry for a somewhat difficult answer to your difficult question.

John Oakes