Do Music Genres Exist?

Of course you can label art - it's how one distinguishes between different types of art. It's categorizing, not passing judgment, which I think is where people get hung up. I have folders on my computer - television, music, games, etc. The files inside are no different for being labeled - just easier to find. The same with musical genres.
I don't believe you have to be an independent artist to be indie, although most indie artists start out this way, releasing home-made recordings, not tied to any mainstream label. But to define an artist based on their means of distribution or recording is asinine. If Green Day dropped from their label and went independent, I would still consider them pop-punk more than anything else.
But indie rock definitely has a different sound - not as heavy as the alternative rock of the 90's, but not as poppy as the pop music of, well, any era. I don't see what the issue with labeling music or art is, and I don't see why 'indie rock' can't exist, as some say. It does exist, and so does alternative, and emo (although probably not in the way people think). But I defend indie rock - it's real, and I listen to it.