Indicator sentences: I am not sure what you mean by "applying the same provision to everyone."
Indicator sentences: What do you mean by this?
Trigger words: state's constitution and policies
Indicator sentences: Is there a chance you could elaborate on what you mean by "the state's constitution and policies"?
Negotiation parts: In a (theoretical) communist state everybody would have equal access to resources, whereas in a capitalist state there is a divide between rich and poor. The choice of capitalism is better for the citizenry as a whole, however some of the citizenry are inevitably born into poverty. Therefore, some citizens are disadvantaged as a result of the state implementing policies which support capitalism over communism. Poverty, with it's obvious disadvantages, is therefore a result of state policy, and should be compensated for as much as possible by the state. You could make similar comparisons with anarchy, feudalism, etc.
Trigger words: equality of opportunity
Indicator sentences: Correct me if I'm wrong, but your problem seems to be with an absolutist extreme definition of "Equality of Opportunity."
Negotiation parts: I have really seen anyone outside of political commentators, philosophers, and sci-fi writers (Gattaca..) , to concerned about it. Lets continue your education example. If you are entirely better suited for a certain profession than I am, but that profession requires a college degree. And I come from a rich family, in a rich school district and my parents afforded me the opportunity to be tutored through high school and prepping for the SATs. And you had none of these advantages. What would be a decent, or common sense approach to college admissions be? I know colleges can not reliably measure very advantage, disadvantage, and make admissions absolute equal opportunities. But they can do something Like the University of Texas did, accept the top 3% of graduates from each Texas high school. This provides a more common use of equal opportunity.