Many times on this site have I heard something described as a 'peeve'. My sense is that this is American.
Although the verb, usually in the passive - he was peeved because he had been given the wrong change, and refused to visit the shop again - exists in Britain, I have seldom heard it used as a noun.
The usual term in Britain I would have said was a 'gripe'. Is a 'peeve' the same thing as a 'gripe'?
Nonetheless I think both expressions are over-the-top for the examples which sometimes appear here. I would tend to call most of them 'pet dislikes'. I think 'peeve' or 'gripe' places too strong a negative sense upon them. A normal healthy mind has likes and dislikes. Dislikes do not have to be justified. In most English-speaking lands people are free to state their preferences.