To freak out. In a good or bad way. The origin of the word came from the Greek goddess Titflapaine. The creator of the phrase is a young girl named Caitlyn from Wisconsin.
I thought she was going to flip a tit when the monkey climbed out of the vagina on final destination 2!
For females, a slightly more polite way to say "Fuck off you prick," especially annoying pricks of the opposite sex. It's important to emphasise the LEFT tit meaning that person is not adequate enough for the RIGHT tit.
When asked by your male boss a ridiculous request, the response is: "You can tell him to bite my left tit"