Typically we say we’re proud of our accomplishments, like completing a piece of art or getting a well-deserved promotion. In that context, it doesn’t make sense to be “proud” of being gay, bi or trans, since it’s a characteristic you have no control over.
But the context in this case is different. In this case, “I’m proud” is a response to “you should be ashamed”.
If being LGBT were not a big deal in our society, there would be no Pride parades, no “Allies”, and of course nobody would claim to be proud of being gay, as nobody today is claiming to be proud of having brown eyes.
If the goal of Pride is accomplished, Pride will no longer be needed.
Until then, if you’re tired of seeing people around you celebrate Pride, try to remember how lucky you are to have no need for it.