Sexual dimorphism is incredibly common in the animal kingdom, and humans are not an exception.

You are setting up a non-falsifiable belief system that asserts that men and women cannot be different above the neck. If that's what lets you sleep at night, who am I to deny you your comforting faith?

But you are fighting against mountains of evidence for cognitive differences between men and women. Are they all cultural? I'm friends with a few post-treatment transgendered people, and I'm inclined to believe at least that hormones have a powerful impact on personality.