More specifically: he is furious that he was humiliated by a woman.
Because humiliating women is part of his imminent being, thus his status quo has been challenged, and he fuckin' hates that someone beneath him doesn't "know their place."
if you zoom in on the one (handshake) at the debate you can see that Harris turned his hand inward. this is a pretty common step to establishing dominance. she's smart enough to know this.
Literally happens as they are introduced in the beginning of the debate. Shouldn't be hard to find. If I had better internet I would link you with timestamp