Somebody that either says everything you just said, or at times even tries to say something you thought of before you could say it with the help of a psychic friend, all to gain credit for doing so.
The parrot mouth wanted to claim the other person's ideas as his/her own, and found that the best way to keep the other person ostracized (or from finding any sort of rhythm) was to just mindlessly blurt out everything the other person just said back them and anybody else present (Baaa I'm not ignorant you're ignorant, Baaa I'm not the pee pee head you're the pee pee head). That way the parrot mouth won either way by remaining relevant via credit or attention from others.