I always thought I wasn't an argumentative person until I figured out that refusing to communicate while thinking vile thoughts is a damn angry response that was way more destructive in my relationships than having a verbal, but civil, argument.

If you weren't angry, you wouldn't be thinking, "OMG, just shut up," while turning on the silent uncommunicative treatment. It's just a cold form of anger instead of a hot one.

Learning how to disagree in a more agreeable manner than shouting or turning the cold shoulder was a really important part of getting better for me. Maybe that's what your therapist was trying to show you.

ETA: Now, I get angry about far fewer things. Some I just let go because they're not really important, more just irritations when I already feel irritable, like with PMS. I can now discuss and disagree without yelling or feeling all adenalized. Maybe once every two or three years, my H and I will have a shouting match and we usually start laughing about halfway through because we both realize we were both irritable at the same time over small things that weren't important. But when it comes to the important things, we can talk and disagree without really arguing or shouting or getting resentful. I couldn't do that before without getting upset inside. So, yeah, getting over my persona of being someone who didn't argue was really important for me.