No one is saying white people can't be proud of their heritage. They can be proud, and they do celebrate their heritage all the time. Acknowledging someone's race isn't extending racism, it's embracing them and their culture.
To be honest I used to think similarly, I never got why people had to be proud of their race, or why it was part of their identity. Eventually I realized it's because the dominant culture is white, I don't have to ask myself what it means to be white or what it means to be american. It is part of my identity, I just have the luxury of not having to think about it.
Anyway, I would highly recommend watching "The Color of Fear", it changed my mind on a lot of stuff I'd never thought about critically.