I don’t think that’s quite right. Pride as a word clearly has some scope as to its use. If one takes pride in oneself it means to value oneself - to have self esteem and like yourself. That’s someone we should all aim for.Which is a large part of the point, since everything you've just written applies equally well to gay pride for exactly the same reasons. As you say yourself, "X pride" implies there is something wrong with being not X. That's why a person is proud of being X, for whatever value of X. A person can't be proud of X unless they regard it as being better than not-X. If they don't, there is no reason for pride.
So when someone says they are proud of, for example, being gay, they are saying “I am not ashamed of that part of me - I like that part of me”. And that’s great. I don’t think there is any sense of superiority in it at all. It’s not saying “I’d rather be gay than not gay” either.