@OP: I'm pretty sure they don't literally mean all genres and subgenres of music, nor do they mean Nickelback to Black Eyed Peas. I tend to say that I like "a lot of music" just because I never want to say one genre. My reasoning, and I'm sure it's theirs too, is that they're open to listening to any kind of music thrown their way.
As for the desensitization, it's not the music that's doing it, but the radio and television channels promoting it. People nowadays generally like that kind of music. Personally, it's not my favourite, but I don't absolutely hate it.
And you can't negatively criticize the popularity of modern music just because it's popular. It's not bad, you just don't like it. Look at how everybody is gawking over those oldies from the 70s and 80s. Frankly, I find those people to be more annoying than the ones who enjoy modern music. At least they're living with the current world.
Still, my favourite types of music are alternate rock/post-grunge/nu metal/trance.