I grew up listening to the Eagles. But in all reality, their careers were over by the time I entered high school, if not long before. Out of all the folks who have passed lately I think I'll miss Alan Rickman the most, because he was a delight to watch in any role.
However, I don't know if I'm really broken up about it. I see lots of people all upset over Bowie, and Rickman, and the other folks who have died lately, while my reaction has been one more of "Oh damn, that sucks."
I think it's because A) as a Catholic, I don't believe that death is the end. It's just a transition.
And B) People die. Careers die, and I think Glenn Frey's career died long before he did. That doesn't mean I don't like his music, or that he didn't have talent; he had tons of talent, and I've spent hours singing along to a lot of his songs. But there's new music coming out every day. I'll be quoting Alan Rickman until the day I die (....and CALL OFF CHRISTMAS!") but there are other actors still making a name for themselves who I'll enjoy next year.
Life is a cycle. The world keeps turning. Nothing we can do will stop that.