Loaded questions, all.
Here’s something to consider: my personal preferences are not automatically someone else’s; your personal preferences are not necessarily my fact. Ergo, when we claim to be learning about music, we must put aside those personal preferences all together. Appreciation of music comes down to this: it’s the way you listen, not what you listen to; it’s the search for the answer to the question “why?”; it’s music education in its purest form.
Nobody has to convince you that you like a certain artist, you already know that. Knowing that, then, is a good place to start. The next, and most important question, is: why do you like certain music?
Is it just the beat? Is it the intricate interplay of voices or instruments? Is it the arrangement? Is it the production values? Is it the songwriting? Is it the lyrics? Is it the melody? Is it the fact that you can sing along easily? Is it all or none of the above?
When music is popular, that means a lot of people like it. That’s an obvious statement. On the other hand, if you can’t listen to a style of music and figure out why it’s popular, you’ll never learn anything from it. You’ll never be able to work in that style, and you’ll be that much poorer in your general music education.
Personal example: I dislike bluegrass. Did I just hear a gasp? Regardless, I once set myself the task to listen to a 3-hour bluegrass program on a local public radio station, every week for about two years. When I started to listen for what made this music what it was, I found a whole new, fascinating mother lode of techniques. Being a guitarist whose music incorporates jazz/folk/classical influences anyway, I started to learn some of the hammer-on riffs and lead fills that bluegrass musicians use regularly. After working them out, I then took it back into my own music to see how I could make it part of my personal style. My music expanded.
When you start to compare songwriting techniques of (say) the Beatles with Billy Joe Armstrong (Green Day), you may run into a bit of a stylistic preference problem. You may not. Either way, it makes absolutely no difference whether you like one, both or either of these artists. What matters is, can you get past your preferences to take a look at what they wrote and how they wrote it? Use the list of questions above as a place to start.
Bottom line: As musicians, we grow or we grow stale. Music is always changing and there’ll always be something new coming along that a previous generation of musicians rejects off-hand as not worth their attention. Don’t fall into that trap. Listen to everything. Learn to appreciate. Then, like whatever you want.