Obviously, each of us has his or her own answer to this question. When I am asked I tell students that the way we talk changes rapidly and, because there is a solid cultural reason that we need to understand what people read and wrote a few hundred years ago, academics have a valid reason for slowing change in the English language. I'd be interested to learn what others say.
This depends on your audience, of course, but, assuming we're dealing with younger students, I wouldn't attempt to motivate them by explaining that they'll need to understand proper grammar so they can read and understand what people wrote centuries ago. After all, we're dealing with a generation where it's often a small victory when you can get them to read a book before watching the movie.
There's something to be said about proper grammar, though, particularly when it's time to start a profession, or even get a job. I remind my kids, "When you turn in a job application, it's probably going into a stack with 50 others. How will your application stand out, to the point where it gets pulled off the applicant pile, and put into the candidate pile?" When the application form asks, "Why do you want to work for our company?" and you can't muster anything much better than an internet cat ("Bcuz i need ca$h"), there's a good chance your application will collect dust for a long time. If you have a strong command of language, though – if you can be articulate, precise, and grammatical – you stand a much better chance of rising above your peers from the outset.
Sure, language evolves, but that's not a good excuse to remain ignorant.
As for slowing down change, I don't mind language evolving, but I'd rather not see it devolve. It's one thing to see a dictionary's usage panel gradually accept a new usage of a word, it's another to plainly sound unintelligent. Everyone will draw their own lines between what makes them bristle and where they are comfortable. Personally, I don't find the use of fun as an adjective particularly irritating, but I'd rather hear fingernails scrape across a chalkboard than hear funner in a sentence. But that's just me. If everyone drew their acceptability boundaries in the same place, there'd probably be little need for ELU.
My answer is similar to J.R.'s, except my students read voraciously, and still do. One of my students, my son, gave me a book he enjoyed greatly: The Road, by Cormac McCarthy. For about a year, I was unable to read it; it is full of sentence fragments. Regarding punctuation, he said, “I believe in periods, in capitals, in the occasional comma, and that’s it.” While I loved His All the Pretty Horses, he takes it too far in the Road.
Where grammar is concerned, as a Latin teacher, I was unmoving. I always told my students that there would come a day that they would need to impress my generation with their command of the English Language. Here I agree completely with J.R. To stand out is a good thing. As for motivating others, it's like the best reason for etiquette - it puts people at ease. If you speak clearly and well, your audience won't struggle to understand your meaning.