While you have your own way of doing it, teabagging is the universal symbol for it. If I walked past some guy who I want to humiliate, wasting a sticky grenade on him will make me look retarded; vice versa if I was the dead guy. Teabagging, though, is something everybody understands. The moment your ragdolled, awkward's body is met with my Spartan's groin, is something everybody understands and thus why it is done the most.
By being the universal symbol for 'i *** your mom last night you suck kid', there is no reason to do anything else as humiliation and all you will end up doing is making a fool of yourself in their eyes. That's why teabagging is done the most.
As for why it's called teabagging...well, balls are held in bags. And I guess going up and down happens in both video game teabagging and real life teabagging.
As for if you're being a girl, well, the fact that girls don't have balls usually increases the humiliation factor.