I know I'm responding to AC but this one I can't let stand.
The Socialism ideal is that everyone doesn't have equal opportunity because the economy is a zero-sum game and some people have a head start by being born into a good family and that through government/societal intervention we can make outcomes for everyone equally good by lowering the amazing outcomes of some (The people with a leg up in life and a few outliers) through tax and using that money to pay for social programs that help the people in society with the lowest outcomes achieve better outcomes regardless of opportunity bias. In this idea you are saying that if you are born to a lower income family no matter how hard you try you will never do as well as that white kid born to a millionaire because he had such a head start and without societal intervention there can be no equal opportunity. And since the economy is a zero-sum game there always has to be winners and losers, so we have to balance out the equation for fairness.
By saying that everyone has an equal Opportunity to rise to the top we are not saying that they can achieve that goal, as socialism does, but that you can try. And if you try really hard you should be able to rise to the top, but some may have to try harder than others and those who don't try will never achieve good outcomes. It is the antithesis of Socialist thought. The difference is equality of outcomes vs equality of opportunity for upward mobility.
Ok Rant done.