That's the thing! I'm mashing X and skipping past all that, and then there is a glitch where the menu doesn't appear for like 10 seconds and I'm stuck there looking at the character, waiting for the menu to appear, and if my opponent immediately rematches, the countdown starts but I still can't do anything until the countdown hits 0, after which the menu will appear with "fight again" greyed out. I can only rematch them if they don't immediately rematch me. In that case I'll still be stuck for 10 seconds before my menu appears but since my opponent hasn't started the countdown, or starts it half way through the 10 second glitch, I can hit "fight again" before the clock hits 0. I hope I'm explaining that well, it's confusing.
Anyway, I appreciate the help werewolfgold! It doesn't look like anybody else has this issue or knows how to help : (