Is it normal for a broken up couple to act like they're still dating even if the guy has a new boyfriend?

Kind of, unfortunately. But girls like that really irritate me. It usually means they got bored with the guy they were with so they moved on, but now they're trying to hold on to both of them. Its totally unfair to both guys. If the ex-boyfriend is the one doing the pursuing, then he's kind of a jerk too and needs to let her move on.