Last night during our dance lesson - tango, my partner appeared to be falling forward onto me...he was off balance, and extremely dramatic. This is very typical behaviour. He is a much more accomplished dancer than I so in the past tended to blame all of his issues on me. It turned out the issue was entirely his, however, my issue is that I PUSHED him away from far too aggressively. My anger both surprised and scared me. Has anyone ever had such issues, and what did you do with it?

Don't know what happened in this situation, but off balance in tango is often a result of either the lady letting her weight move back to her heel (it should be forward in the foot until the step off the foot is nearly complete) or of the man stepping directly at the lady, rather than into the diagonal CBMP or side lead positions required for tango movement.

As for the anger, have you been frustrated by something like this for some time now, and it all came out at once? You need to work together, and most likely with the coach, to solve the things that are making each of you uncomfortable - can't constantly nag partner, but can't hold concerns in either.