I don't think its necessarily that things come with age.
Rowan provides a good point that very well could associate music coming with the older you get, like maturity and knowledge.
But for me Music comes with TIME. Which is almost essentially the same thing because time only moves in one direction, but lets say we never age, but time is still there.
I didn't immediately like dubstep the first time i heard it, nor the second time, but as time went on i grew more and more into its liking.
Same goes for Metalcore & Anthony Green's voice, it didn't come with age, because most of those things happened within a very short time (2-3 months). It came with repetition of hearing that type of music.

Nor am i saying that its just repetition, but i think it has a lot to do with it.