nah, i'm all in favor of equal opportunity. i just don't like the concept of the state having to provide it.
now tell me i'm an idiot (been there all day so i shouldn't be affected anymore), but i really find the whole concept of compassionate conservatism very appealing. people should make their own decisions and good will come out of it. in the case of schooling, for example, i'd like to see a privately run school system where good schools further invest in their reputation by way of offering scholarships to deserving but poor kids: so if you're rich and you want to go to the good school you pay your fees and implicitly decide to subsidize the poorer students, if you're an alumnus who succeeded in the world and want to contribute to the school prestige you set up your own scholarship, and if you're a school manager you go knocking on doors (companies, public institutions, churches, whatever) and ask for money for these scholarships. this is what choice is about: letting individuals have power over the transfers they make, so that they can decide to help others if they want, and mind their own business if they don't.
as for poverty, of course you are right. i agree on the fact that the state should let people out of deprivation, for the reason you cite (although i would resort to government only if private charities fail, and i redirect you to any good republican website for the well-known argument about involvement and dedication versus obligation). but poverty and inequality are two different problems altogether - read the works of martin feldstein for a persuasive explanation, he won the nobel prize while i never did so probably he's more to the point than i could ever be.
now, the typical point that is made against the whole small-government stand is: people are evil, so they won't really provide for others unless forced. i don't agree, and i could expound for pages on this, but i need to go to bed so i'll just say that i recognize that this point is based ethically, so it's pre-analytical and you sort of either believe it or not (but no, you're not stupid if you don't).