Lots of prejudgements here on both sides of the debate.
I think that ultimately, all parents on this forum, just by the sheer fact that we are concerned about being a good parent to join a forum about parenting, care deeply about our children and want only what is "best" for them. Now, the definition of "best" is much more personal.
I am an American transplant here in London, and thus my outlook might be different from many of you here.
I was a product of an expensive all-girls private school, more expensive big name college (small University in the US), and an even more expensive Ivy medical school. My parents could have sent me to the local state school, as we lived in a nice area and thus had a very nice state school (swimming pool, theatre, ice skating rink, tennis courts...all at a state school!), but chose to send me to a private school because I was a very shy child and the student/teacher ratio is much smaller at a private school. They also felt that bullying and racism (I'm oriental, and they always feared me being exposed to hurtful comments caused by ignorance) would be more checked at a small private school.
They were right. I absolutely adored my school, and was exposed to positive female role models and wonderfully supportive teachers. The types of classes that were offered were amazing...for example, I took a seminar on Milton's Paradise Lost with was interclass (I was a sophmore, and there was a 2 juniors, and 1 senior also in the class) Total of 4 students and 1 teacher made up the class...it was much more like a university class than a high school one.
My excellent secondary school made it easier for me to get into the excellent college, which madie it easier to get my research opportunity at a top teaching hospital in Boston, which made is easier to get into my medical school. The key phrase is "made it easier", not made it possible.
Not all private schools are good, and not all state schools are bad. I think that we as parents shouldn't dismiss either, must make the best choice, assuming the choice is available, based on the ability, personality of the particular child, as well as personal situations.