I think I understand what you are saying, but I believe it is my duty as a father to giver my daughter every advantage possible, which is the opposite of equality of opportunity. But it's also my duty to ensure that she doesn't end up in the position of Anastasia Romanov.
And yes, that's very much what I did mean: A rationally self-interested sort and degree of egalitarianism which anyone with adaptive cognitive traits adequate to survival can find some way to rationalize within their ideology. Certainly equalizers which involve lifting all boats are much more in the vein of win-win than are equalizers which involve sinking all boats.
I might even go further personally, although I won't ask anyone else to do so: I too try to give my daughter every reasonable advantage which will not corrupt her or rob someone else. One of those advantages is the advantage of an example of -- dare I say it? will the spectre of ayn rand come and suck all the green ink from my veins? -- altruistic behaviour, and its rewards in life. By altruistic behaviour I do not mean pathological monomania.