Works both ways, but maybe you can't see it within yourself. You tend to drop sarcastic little bombs very often, which I'm getting better at just ignoring or giving just a quick comeback and moving on. A truly compassionate person can get very angry at times if they feel that the other is not being fair to them or to others, so you're conflating "compassion" with "anger", and they ain't the same.
But I agree that my temper can ramp up pretty quickly, and it is something that I long have to work on to keep it in check. In real life (i.e. not here) I very rarely "lose it". My wife and I have been married for 48 years, and only once in that period of time did we ever go to bed angry with each other-- and then we laughed the next morning because we had a hard time remembering what we were arguing about.