In Dracula, van Helsing goes on and on about how the vampire has a "child brain", implying not only does it not mature over the centuries, but it actually regresses to an emotionally and mentally less mature state than a human adult would be.

In Twilight the high school thing is specifically because of the not growing physically. Nothing to do with mental.

They realized if they start in high school they can stay in one place longer. It adds more time they can be there without seeming weird. They go to both high school and college and then move on to a new place.

Ew. That one's the worst, honestly. "Vampire", bah. An immortal pedo is still a pedo, just for far longer.