Is there an evolutionary basis for why women mature faster than men?
Reproduction is kind of the definition of biological success. Logically, it works because it works because it works. Provided that the mother is responsible and healthy, there's a good chance the offspring will survive and reproduce. And since health and age are like opposing forces, the sooner a female develops and develops responsibility, the more likely they will be to reproduce and supply viable offspring to the population.

Similarly, males remain verile for many years past their prime. Since it doesn't matter (as much) whether the father survives child birth, his health is less important. More important (genetically) is the spread of his DNA. The more time a male has to do that the more his DNA will spread. So why not start earlier? Reproducing for an extra ten or twenty years will cause the spread of a much greater amount of DNA than 1 or 2 years early on, and (plausibly) since the male often has a dangerous occupation, males that develop(ed) later (when their size/strength was greater), probably help(ed) ensure the males' survival.

And there is something to say about sexual preference. It is likely that the males' disposition toward healthy females and a females' dispositon toward successful males is genetic... much like a bird who sings the best song. Why? Because it is/was a successful cascade of events.