I don't know about ''incompatible'' but yes, therapy is not for everyone and/or might not 'work' for everyone.

There are a lot of misconceptions in what you believe. For one, therapy does not ask nor require anyone to drop their anger in order to be 'weak' and depressed. I don't know what type of therapy would advocate that in the first place. Therapy aims to empower, never to make anyone weak. Likewise, being vulnerable does not equate to being 'weak' or as you say "helpless" and "defenseless". It actually requires a lot of strength to stand in your truth, warts and all.

It seems you are using anger to operate in the world and mistakenly believe that using anger means: strength, high self-esteem and being functional. Reading what you write, it actually seems you are using your anger as a defense that is masking something because to you, contemplating anything else is weak or helpless etc. Being stuck in this one mode, THAT is what indicates weakness - not being flexible or adaptable and functioning in a rigid way all the time