Could you please point out where I'm making these claims? Usually, clear proof is necessary from those who are making these claims.That is all you got is God is unchanging? You need to provide clear proof of a Son of God before the Word became flesh?
Regardless, logic works just fine with me. An unchanging god cannot become a father. God is either eternally the father or he must change. If he suddenly becomes a father, then prior to that moment he was eternally alone.
Now I will be the first to point out that God doesn't need anyone so he very well spend eternity alone. It just doesn't strike me as a very loving god.