Well, I can think of a few reasons:
I. Music is one of those special interests that's socially acceptable and quite wide spread, so it's like an aspie talking about trains or My Little Pony or ancient Egypt or whatever their current thing is, but with a higher chance that the person they're talking to will share the interest or, if they don't, will pretend to.
II. If the person they're talking to shares the interest, it gives them something to talk about and over which they can bond. Obviously this doesn't apply to you.
III. If there is a shared interest, then they can bond by introducing you to music they're familiar with but you aren't, creating further opportunities for bonding by talking about the music once you've listened to it. This also allows the guy to "give" the girl something (even if it's only knowledge of a new band or the like) which is important to many guys when they become romantically interested in someone. It's a way of demonstrating their interest in you.
IV. If there is a shared interest in a particular band or artist, it opens up possibilities for going out together to concerts or shows. If a girl is into Justin Bieber for example, getting tickets to one of Bieber's concerts is something that's pretty much guaranteed to go over well.
Most of the above also applies to other interests than just music, but as I said, music is a socially approved and relatively wide-spread special interest.
I don't have any particular interest in music and I've had a couple of girls who've decided they needed to "educate" me and introduce me to all the music they like. I didn't mind the music and enjoyed spending time with them, so it was all good. And music serves as a memory trigger — at least for me — so when I hear a particular song, I remember the first time I heard it with one of these girls and that was generally pretty good and can lift my spirits. Of course, the fact that the relationships didn't last is a bit of downer, but not enough to overwhelm the pleasant memory.