A parable of sorts:
Two athletes, of equal talent, want to race in the 100 metre hurdles at the Olympics. One of the runners, because his father sits on the US Olympic qualifying board (or whatever), gets his son a spot in the finals without having to go through all of the qualifying heats. The other runner, who doesn't have any connections, has to go through all of those heats, as does everyone else. Maybe he makes it, and maybe he doesn't, but by the time the final rolls around, he has nothing left in the tank. Oh, he tries hard, sure - but the kid who got the free pass wins. They had the same opportunity, in that final race to win it all. Same starting line and so forth. But it wasn't the same situation.
Imagine the race again, only this time everyone can enter without qualifying heats. That seems more fair. But then imagine that final race where a few people get a 95 metre head start, and everyone else starts at the beginning. Or a race where one runner gets to use hurdles that are only six inches tall, while everyone else has to jump the standard ones.
Equality of opportunity is meaningless unless one has equality of situation. The two are not mutually exclusive; indeed, the latter is the precondition for the former.