Some people just like not wearing shirts. It is inherently about having been marginalized and afraid, and about being more open, more connected, and less afraid. That aspect of pride isn't inherently gay. It exists as an event to encourage openness and freedom, have a celebratory atmosphere, boost self-esteem for those involved, and also campaign for civil rights. Pride may be 'for everyone,' but it still has a spirit and an aim. There were more 'polite, respectable' focused gay movements before, and there still are, but Pride isn't just tied to them.
It is a more radical-spirited event, because that is its history. Considering the history of Pride, I think it's because 'The first Pride was a riot.' The pride parade in '70 commemorated/continued in the spirit of the riot, and of the subsequent demonstrations in Greenwich Village during '69.
