You really can tell quite a lot about a person just by learning what music they choose to listen to. It's always fascinated me, really.
I believe the music you choose to listen to really does matter, because it can have a profound effect on your mood. If you listen to nothing but loud violent angry music in headphones day in and day out for months, it's likely to make you a bit of an angry person. If you listen to nothing but slow paced dinner jazz at a low volume, you're likely to be quite a bit more calm. I feel like the existence of genres helps divide music into very specific categories of mood.
You're having trouble finding music that you like on the radio because most of what they play on the radio is garbage of the moment to fill the void between commercials. Exploring music and discovering what appeals to you specifically can be one of the most rich experiences of your life, in my opinion.