Why is it wrong to say I'm embarrassed to be white?

I randomly remembered a conversation I had with my Filipino friend when we were talking about racism. We were specifically talking about the fact that some white people think they experience racism when all it does is hurt their feelings (its nothing compared to hate crimes and... everything else POC go through)

In that conversation, I half-jokingly told her it was embarrassing to be white, considering how so many white people are entitled and racist. She got offended and wouldn't really tell me why. Could someone explain why this is wrong to say? I don't wish I was another race, but I'm not proud to be white.