The only way to prove that all people have equal opportunity is for all people to have equal results. If one person achieves more than another does, it is only because the one person had some sort of unfair advantage: a better school, better parenting, a richer famility, a distaste for drugs, etc.
Since we cannot ensure all people produce at the same level, we must equalize things by ensuring that the fruits of all labor is collectivized and distributed evenly. This is how we make up for the unfair differences in abilities. The person who was denied the same opportunities as others still gets to enjoy the same results.