Sorry, but this question is super-broad and it only has me imagining endless reasons why not and other smarty responses.
They’d need one less piece of equipment on space walks. Unless the reason was that there was actually air up there, in which case… the universe and/or physics would be very different, or else, for example, we’d be crushed by the weight of all the air above us.
If it was just that we didn’t need air, then our astronauts would still die of cold and radiation and lack of pressure up there, unless we had suits, so not much difference. In other words, not having air to breathe is only one of the relatively minor barriers to doing things in space.
If you just want help to fantasize about people flying around in the sky doing fantastic stuff, maybe watch the 1980’s film Flash Gordon which has hawk men flying around and stuff, and a hilarious theme song.