This is called repression, and it's a type of masking that even neurotypicals do frequently. You're not actually calm and you're not actually getting rid of the anger, you're just bottling it up.

You might not be aware that you're expressing that anger, but you absolutely are. A lot of angry, angry people don't even realize they're constantly putting their aggression onto others. Everyone repressing their anger is constantly radiating particles of Big Mad.

If it's eating you up inside, it did actually bother you. You need to process your emotions instead of pushing them down.