Egalitarianism
Actually I'd say that egalitarianism asserts the latter rather than the former. That is, egalitarianism, as a political concept, is a practical paradigm rather than an explanatory one. To the egalitarian it genuinely doesn't matter whether people are indeed "equal to each other"; all that matters is that society treat them equally.
I think the error you're making is in assuming that those two concepts must be linked. That equal treatment by society must be founded on a conception of humanity as fundamentally equal. I think that's a backwards (albeit unfortunately common) way of looking at things.
Human beings exist within a social matrix, individual beings constitute atomic elements of that matrix. Each element is both indivisible and unique; from a structural perspective, our civilization is actually rather simplistic.
Now, the reality of human interpersonal bonds get much much messier than that simplistic overview would suggest, but the broad outline holds. Each individual member of society has an equal share of societal interest because he holds an equal share of societal interest. Society only exists to bennefit the individuals that compose it, as optimally as possible. Therefore the ideal social paradigm is one which maximizes in every direction.
This is a tad more mathematical than one is used to getting in a discussion on social sciences, but we're dealing with a fundamental issue here so it's useful to stick with basics. Individual human beings constitute the natural class of our society, full stop. And like any natural class, humanity is viable as a hash unit in computation, meaning that what's good for one person is generally good for another.
All of which leads us to the conclusion that a person's entitlements from society emerge not from any natural resevoir of quantitative persobal "talent", but of binary membership in that category called human society.
If you're part of society, society must look out for you. What you do within that is entirely up to you. Your "superiority", "inferiority", or "equality" is wholly irrelevent.
Why not, indeed! Class society naturally encourages attempts at status shifts.
And many, many, many people over the centuries have tried exactly that which you propose. Most of them failed, of course, but a good number achieved. Generation after generation there have been stories of "new money" and "overnight billionaires". No one ever said that the class system was frozen.
But it's nonetheless pretty solid, and it only lets in so many, so often. The point of "group force", as you put it, is to circumvent that bottleneck and impose a new system from above. It's the reason the bourgeoisie overthrew the arisotcracy at Bastille. It's the reason the United States declared itself independent.
Washington and Jefferson could have tried to rise through the ranks of British society. Both were, in fact, from respectable houses. Washington was even a Lieutenant General in the Colonial Army. But they decided that they (and their interests, which psychologically are really one in the same) could be better served by "instituting new government". So they threw out the British and established a new country with themselves in charge.
"Group force" worked! And it helped to inspire a liberal awakening across the European world.
Political revolution isn't about getting a job, it's about remaking the entire order of things. It's about re-crafting the very foundations of society. That's a pretty big undertaking and one that needs to be done every time to time. And indeed usually is only occurs when all other, easier, avenues of change, have been exhausted.
Societies pursue radical revolution when their institutions are no longer capable of serving their interests regardless of how they are organized. We are radically approaching such a state in the first world.
Now if the state of the world doesn't interest you, you can sit at home and watch American Idol all day. Abstinence is always an option. But "group force" will go on. "Group force" is what built your country, and mine, and it's what freed ten million slaves from bondage and gave them the right to vote. It's what overthrew the Czars and crushed Hitler.
I choose "group force" because it works.
