why do people care so much about trophies and achievements?

No idea, I personally enjoy the games I play but not because of the achievements or trophies but the story and because of how fun the game is. 
If I played because of the Achievements or Trophies the game must suck really really bad. 

Because if I do all the races in Forza 3 I will have 1000/1000 and Adriana Lima will divorce that basketball player and get with me instead. Right?

Oh hey, this topic again.
 
I like achievements but I will absolutely play a game without one, and I will not buy a game just for easy achievements.
 
When done right (and/or approached in the right way), they add to replay value, make side missions and messing around more rewarding, and encourage the player to change up his style.
When done wrong (and/or approached in the wrong way), they increase tedium, give incentive to a boring task, and encourage players to boost online and ruin competitive matches.
 
Ever gone for a high score in the arcade? Ever speedrun that level in Perfect Dark to get infinite ammo with no reloads? Ever get 100% completion just for the hell of it?
It's the same damn thing - except streamlined and standardized.

It baffles me that people still ask this question. Sure the points don't mean anything, but as others have said the points in Donkey Kong (for example) didn't mean anything either and yet people strove (and still do strive) to reach a high score. Why? I suspect the answer is different for different people (natch). I know you didn't like the "opinion" answer but that's really what it comes down to. You don't think achievements are engaging, but others do. Maybe you don't like guacamole, but others do. Same thing. 
 
For me, I like unlocking the icons. I like looking at a list of things I did in a game. It's a way to help me remember how much I liked (or even didn't so much like) a game. Many times games will slip from my memory and looking through my achievements helps jog that memory. I like that achievements extend the life of a game. Instead of tossing it aside after completing the "main quest", I have other challenges I can try to accomplish. Sure, sometimes the achievements are ridiculous and are out of reach. In those cases I don't bother. I also won't decide to buy or not buy a game or DLC just based on achievements, but they are important to me.
 
Bottom line is they're fun for me which is really all that matters to me. :)