Question: How is someone who is born into a class of lower economic means able to go to a top university, and how will universities be able to get the highest intellectuals if everyone is not given the same education and opportunities? The class system is something inherent in the capitalist system, and those who have are given much more freedom and choices than those who have not.
Answer: First, in a free society there really isn't as much of a class system as you may think. The correlation between a person's income and that of his grandparents is extremely low. Indeed, it is more likely you won't have wealth or earnings like your grandparents than it is that you will. And this goes for wealthy people, by and large, as much as for poor people. Of course there are exceptions, but that doesn't change the general social characteristic.
But while this should ease your mind a bit, it isn't the fundamental issue. You want to know why some children are entitled to an easier or better education than others. But the entitlement is not the children's: it is the entitlement of those giving the education.
Any child depends on others for support and education. In the Objectivist view, parents are obligated to provide a reasonable minimum in this regard, but beyond that parents have the right to vary the degree of their investment. And others are free to invest in the child's education as they choose and the parents permit.
Who will support meritorious children and young adults in seeking a good education? Those who care to, or those who can make money from doing so. Those who care to will include philanthropists and universities bent on finding brilliant students.
But let's consider the latter group, though the former have been bountiful. In a free society, it is quite conceivable that poor people with potential should be able to finance their education by taking out loans. The main reason such loans are not widely available now without government support is the personal bankruptcy laws, which show little respect for contracts. Under a system that held people to debt obligations (allowing bankrupts to manage, not evade, debts), loans for education should be a good business. Just as today one can go to professional school on commercial loans, so could one get a college education in a system based on individual freedom and responsibility. Of course, this only works if one graduates from University prepared to get a good job and earn enough to pay back one's loans, but that's how it should be.
In a free society, independence would be rewarded and poor people especially would learn to value education.
And you further should consider the effects of such a system on poverty itself. People have free will, and they can always make mistakes or through misfortune end up in difficult circumstances. But incentives matter. In our system today, government welfare systems have created a class of impoverished dependents who grow up thinking like dependents, without good work skills or a pro-education culture. In a free society, independence would be rewarded and poor people especially would learn to value education. Indeed, we have seen hints of how this would work in the effects of the partial welfare reform on the 1990s. And we have seen how culture matters in experiences of motivated, impoverished immigrant groups who valued education.
So Objectivists envision a society where no one has to apologize for having earned wealth, and where politics is not driven by jealousy. But we also envision a dynamic, vibrant society in which real, grinding poverty is little known and where people live responsible, rational lives taking advantage of opportunity, and where others assist those less fortunate because it is in their own interest to do so.