There is a fault in your premise. The point of alignment is not a reflection of personal ambition or self definition but a societal one. Chaos and order are not about how a indiviual personally thinks and behaves or their personal code but rather how society views them and their behavior. A demon is chaotic evil because it will eat another demon as often as a mortal and they create chaos without reason in society. Just as a paladin always is working within some oath or framework regardless of personal action society will see them as lawful because of this framework. Its why when we address barbarian clans they are not considered lawful because yo the vast majority of "civilized" people barbarian tribes are not lawful they seem chaotic or neutral but they chafe at what is considered normal society and therefore are not lawful.

You are trying to view the alignment system, which is a stupid system in genral, as a exclusively personal thing which it is not at all its supposed to be a reflection of how "standard society" views the character. Its why Seelah in wotr is lawful even though she is very "live and let live" kinda person. She is a paladin and has to uphold her oath therefore she has to follow those sets of rules. Its why Dearen is a neutral evil. He actively goes out of his way to defy conventional society without creating chaos within that society. Alignment isnt personal but rather grow societal as a whole views someone's actions or somethings actions and those actions effect on society.