Ignore him, pretend like he's not there.
Or maybe you guys can learn how to sit and talk? It seems like you're already in for it, so you might as well try it and see how it goes.
If you're moving forward with your relationship with your dad, you're strong. Maybe you cry out of habit or because you're a teenage girl. I'm about the same age as you and I cry when I get in an argument. It's awful, I never finish the argument because i have to run upstairs to my room to cry...