Answer: a definition I found for institutional racism is “the systematic distribution of resources, power and opportunity in our society to the benefit of people who are white and the exclusion of people of color.” Now how does that and the quote reflect white supremacy? Well, their disagreement is rooted in the oppression and denial of people of color. They would rule in favor in a system that benefits them, rather than a system that is distributed evenly and equally for everyone regardless of race, sex, etc.
Most things regarding the oppression of people of color or inequality, or how white people benefit from a system designed for them to succeed and would rather ignore it than address it because they wanna reap the benefits tend to trigger white fragility because I feel like they want to make it clear they aren't racist, homophobic, or whatever before acknowledging their privilege.
