It is by faith we can see and believe that Jesus is God - fully man and fully God.
If that’s what you see and believe by faith then that’s what you see and believe. The problem I have with that is deciding that that’s what other people must see and believe in order to be Christian. That’s the path the RCC took and Protestantism, for the most part, has stayed on that path. There was a time in Church history when what you see and believe isn’t what the Church saw and believed.
The Bible itself doesn’t require anyone to believe “Jesus is God - fully man and fully God.” That comes from the Church; we can locate it in Church history, centuries after the apostles died.
I believe Jesus is God. I believe Jesus is a human person. There’s no room for me in your faith tradition. I would have been persecuted, tortured, and killed by your spiritual ancestors.
Logic doesn't come into this at all…
Logic did come into it for those who eventually developed the doctrine of the hypostatic union.
…just as logically a virgin can't give birth.
With the technology available today, virgins may become pregnant and give birth without engaging in sexual relations with a man.
That technology wasn’t available until late in the 20th century. There are reported cases of women becoming pregnant without having sexual relations with a man. How much stock we should put in those reports is debatable.
Setting all that aside, it’s logical to me that God could miraculously cause a virgin to become pregnant and give birth without the virgin having sexual relations with a man - and perish the thought that God would have to have sexual relations with a virgin in order to work the miracle.
I believe in the virgin birth. I believe Jesus was miraculously begotten by the Father and conceived by the virgin, Mary. That places the origin of Jesus in the womb of his mother.