Everyone likes what they like. You do not need to have a reason as to why some people like option A compared to option B. As long no one is hurting you or others based on their opinions and interests, who gives a hoot? I don't, but I care about my friends' music tastes to get to know them better.
Personally, my music collection goes from everything towards the end of the classical scale to almost heavy metal. I am not a fan of most rap or hip hop, but I can get into the beat. I'm also not a huge fan of what pop has turned into, but I won't judge someone based on what they listen to. Here are 4 reasons why:
1: Maybe they connect with a genre better than you.
Let's face it. Not everyone loves rock. Not everyone loves R&B, and not everyone loves one genre in general.. Except maybe Disney. However, I bet you have a favorite band or two that just seem to get you on a deep level somewhere that no other artist does. You wouldn't want someone telling you your favorite bands are garbage or trash. Don't do it to other people if you can't understand why they connect with that out of the way hardcore screamo band. Just accept it, and recognize that that band is something that they love.
2: Sometimes you can discover a new band
There have been times where I've been hesitant about listening to something from a friend, but I ended up loving it more than them in the end. This happened with a few hard rock and alternative bands in high school. Not only will you have something to talk about with the other person now, but you will understand them on a deeper level than you did before. It'll be worth it. I promise.
3: Music brings people together
Your best friend drags you to a concert for an artist you've never heard of. You're extremely skeptical at first, but then, you end up having the time of your life. Caring about your friend's taste in music just gave you a life experience that you would have never had otherwise if you sat at home and decided to be judgmental instead. You just got friend points, and you may have made new friends in the process. Not a bad deal right?
4: Sharing your music will help people know what you're thinking
Have you ever been in a situation where you cannot express exactly how you're feeling, but a song comes on and it hits you deep where it mattered? Sharing that song with the people that care about you in that moment will make them understand how to help you if you need help. It can help alleviate awkward situations. I even used a song once to get a guy to kiss me, because I was too shy to say it outright. Music helps. Trust me.
Not everyone loves everything. That is a given, but even just appreciating someone else's taste in music can give you a deeper understanding into them as a person. Music brings people together, and sometimes it can heal a hurting heart. It's not a perfect medium to express love and emotion, but it's not far off. Take the time to listen to your friend's, significant other's, parent's, lover's music. You'll get to know them better.