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There is always statistical outliers in any large data set, but they don't affect the median value significantly.

This is in no way a rebuttal to what they said. The point is that privilege very well may exist and be a valid concept surrounding an aggregate, but be a invalid tool for comparing individuals.

Who's using it to compare individuals? The entire discussion revolves around populations and institutions.

Conditionality is applied in the concept: Privilege is essentially the difference in outcomes ascribed to two otherwise identical people due to a particular disadvantage that members of one group suffer but members of the other group don't.

This is also known as an ecological fallacy [0].

[0] https://en.wikipedia.org/wiki/Ecological_fallacy