It's simple math really. As someone above pointed out, a university professor will graduate about 15 PhD's. Since the number of professor positions isn't quickly increasing, most of those PhD's aren't going to become university professors. So they either languish as post-docs or have to find a different job (either in or out of science).
This is good for the universities who can get the cream of the crop as professors. (And considering that getting a PhD in science is no trivial matter in the first place, this is really the cream of the cream of the crop). The bad part is that we've lead a huge number of people down a very challenging path without telling them that their odds of success would have been similar if they chased their dream of becoming a rock star, instead. (OK, maybe not quite, but you get the point).
On top of that, if they are one of the lucky/hardest working/brightest ones who manage to get a university position, they then face a 5-10 trial period before they get tenure, during which 80 hour weeks are the norm as they teach classes, train grad students, get grants, and publish or perish. After tenure, it doesn't get much easier if they want to keep doing research and feed their graduate students.
The easiest way to lower the number of science grad students is probably simply to be honest with them, and let them know this going in, instead of telling kids and young adults how important it is that people go into science. But, if we did that... 1 - the current system would fall apart because grad students (and post-docs) form an extremely valuable class of cheap and highly skilled labor for science research at universities. 2 - The quality of research in general would go down dramatically, as some of the best and brightest possible scientists (i.e., the few who make it, now) would choose other fields.