I'll admit it; I'm fanatical about being grammatical. Spelling, punctuation, syntax...these things are important to me because they can help (or hinder) communication.
Imagine I walk into a room and say, "Apple broomstick waterbug!" to you. You would be mystified, and rightly so, especially if I explained, "That's just how I say hello."
Of course "apple broomstick waterbug" is no way to say hello. And you would be perfectly within your rights to tell me so (and maybe even sock me in the mouth).
I care about grammar for the same reason I care about being a moral person. I hate to do this, but I'm gonna throw an SAT-like comparison at you: Grammar is to language as morality is to behavior. Think about it. You would be just as upset (and even more likely to belt me in the kisser) if I walked into a room and hit you with a chair, explaining, "That's just how I say hello." Morality regulates our behavior. It makes us understood.*
We are born — like it or not — into a social universe. To me, this fact requires us to do our best to be understood and to communicate appropriately, whether that's through proper grammar or by living a moral life. Now, perhaps you say, "What if I don't want to live in a social universe?" To you I reply, fine. Go live in a hole in the desert. Fashion a crude rocket ship and blast yourself into orbit. But if you want to live here, you ought to know the rules. And live by them. Anything else is nonsensical.
"But," you argue (for I am imagining you as an argumentative soul), "I don't want to be sensible. Living logically is for Vulcans.** I want to be wild and crazy!" Again, I reply to you, fine. But the price for not communicating properly, through words or behavior, is to be lonely. You might as well slap me in the face, and everyone else you meet, for that matter.
I can't imagine that anyone truly wants to be alone, separated from the warm, cuddly mass of humankind, but that's precisely what we do when we hamper proper human understanding. Think about that the next time you place an apostrophe where it ought not to be.
* Thanks to Dr. Ernest Colamatti, theology professor extraordinaire, who first made this argument.
** Bonus Trekkie reference. Live long and prosper!