Substance Dualism is the view that there is both a body and a soul/mind. I believe most Christians believe something along the lines of what C.S. Lewis proclaimed, ” you are not your body, you are a soul and you have a body”. This is a rough paraphrase, but works to show the point he was making. All this means is that our soul is essentially what and who we are. Now God is typically considered to have a soul before entering the world. Lastly, Jesus is considered both fully God and fully man. 1. Man is essentially his soul. 2. God has a soul prior to coming in the world. 3. God is fully man and God. 4.When God becomes incarnate he either gains a human soul in addition to his old soul, replaces his God soul with a human soul, or simply keeps his God soul. 5. Any option in 4. contradict premise 2.. Thus, 1. Must be false.
I am not comfortable with rejecting substance Dualism, but I am not sure what else can be done currently.