Bahhh, I'm probably older than a lot of you here (even you adults) and I got into Pokemon in my early to mid teens and I only just NOW started playing the game (Soul Silver).
It's really a mentality, I think, and personality-related.
Some people hate Pokemon (or anything else that is longstanding and has a strong fanbase) simply BECAUSE it is popular. For myself, I tend to dislike cliched stories.
Some people also hate Pokemon because the episodes get repetitive. Let's face it, the Pokemon TV series is really predictable. Some people are okay with it or like it and some people don't. If people are more serious, they probably roll their eyes at the stupid jokes.
Some people hate Pokemon because they think 'it's too childish'. Yes, the series is aimed at children and the themes are very basic, but they still deal with topics that everyone has to deal with - child or adult - and they deal with them in generally tasteful and not overly complicated ways. Pokemon has a simplicity to it that more 'adult' games don't have and it is reflective, I think, of the 'innocence' found in children.
In relation to that, some people think they're 'too mature' to be playing Pokemon. Also, some gamers think they're 'too hardcore' for 'childish' games like Pokemon.
Though in all reality, in comparing a gamer who loves Pokemon and collects Pokemon to a gamer who calls himself/herself a hardcore gamer and who does nothing but run through deathmatches on Unreal Tournament... is the one playing Unreal Tournament really that much more 'mature'?
In my opinion, it makes me grin to see adults having fun with the Pokemon games because it shows me that maybe, they have/kept some of that childlike simplicity/fun/innocence in their lives.
I'll share a brief story to illustrate what I'm trying to explain:
When I went in to the store to pick up my copy of Soul Silver on the first day of release, I was standing in line in front of a bunch of guys who were all 18 and over (I recognized them as being former classmates of my sibling who has since graduated high school for a few years now).
When the cashier asked me what I was there to pick up and I said, "Pokemon Soul Silver!" one of the guys cheered and another one of them yelled out, "Pokemon Heart Gold!"
Everyone was picking up Pokemon!
... And two of group of guys were picking up Bioshock while at it.
Talk about an interesting combination, eh? :)
But it's a true story which just shows that anyone of any age can and could enjoy Pokemon - both as a story and as a game.
For myself as an adult, Pokemon is both a fun game and a challenging game if you get involved in IV breeding and EV training. As a bonus (for me anyways), it's also like a longstanding Tomogatchi in the sense that your Pokemon can love/hate you and you have a 'relationship' with your Pokemon where you 'care' for them and they 'care' for you back.