Maybe what they should have said was "I'm getting sick and tired of all the race discussions" and not deny that racism exists. Racism is going to exist, it's millions of years old, and served evolutionary purpose at one point. Did you know that dog litters will pick on the another dog in the litter who is a different color from the rest? Its purpose may not seem to serve much function now, but people are hard wired to categorize and protect their own. Protecting their own also changes like a radiating circle outward from the self. People have a hierarchy of protective defenses that start with self preservation, preservation of family, then friends, then local community, then country, then world. If aliens attacked nobody would be playing the race card, we would be helping each other. When America was attacked during 9/11 they weren't fixated on racism towards each other; they were in protective mode helping each other and focused on their perceived enemy.
So, if a person feels their race is being attacked they will have a natural drive to protect their like types. When people band together to say "white people are responsible for our oppression" or "black people are all on wellfare" it is going to pull out some protective urge inside you that you didn't even know existed.
The goal is to focus on changing behaviors with positive reinforcement, not bringing social change through guilt and anger. That just forces people to act defensively. As Gandhi said, "be the change you want to see in the world."