Answer: First, disentangle your ego from your child's decision. Yes, you raised him (choosing a gender here for simplicity's sake), and maybe you made some mistakes, but correlations are not one-to-one; it's not as if all parents who make mistakes raise high-school dropouts, and not all college graduates who go on to productive careers have parents who didn't make mistakes.
Second, in the empty space where that negative thinking used to be, put the understanding that people become good parents not by making a certain number of good decisions over the lives of their children, but instead by keeping their heads in the face of whatever their kids throw at them.
Third, don't treat "live and let live" as a fixed approach that dictates sitting mutely on the sidelines. Sometimes it means exactly that, but other times a parent has to intervene; in those cases, "live and let live" means intervening to protect or optimize your child's choices instead of imposing your own.
It's hard to give you specific suggestions when I don't know the specifics, such as how old your child is, why he dropped out, how solid/strained the trust is between you two, whether substance abuse is involved, etc.
But I can suggest that you not say "unjustifiably stupid" out loud — and, if you're on speaking terms, that you explain to your kid that you're not making value judgments, you're just aware of the tough prospects that await people who drop out of high school (the numbers are grim).
Then you can say that some people end up defying these grim numbers, but the key to that is having a plan, which you stand ready to help him establish and pursue. Your financial support can be contingent on his having and sticking to such a plan.
I can also suggest you find the best family therapist out there and get to work (just you for now), to help you distinguish between smart strategies and unproductive battles with a child who drifts off-course.
E-mail Carolyn Hax at firstname.lastname@example.org, follow her on Facebook at www.facebook.com/carolyn.hax or chat with her online at noon each Friday at www.washingtonpost.com.