Why do people pretend that they're not angry

Either passive aggressiveness or they're unaware of how to be assertive so they act out or manipulate. It's weakness basically.

Ways of manipulation

Because there's this stupid mindset nowadays that if you're angry, you've lost something. So if someone makes you made, they "win." The preferred position is "not giving a fuck." It's led to people pretending they aren't angry when they are, or trying to be apathetic and letting people walk all over them because they have to not care.