It's not that white people haven't been insulted, it's just that have not been brought up in a way that would lead to them feeling insulted, based on racial grounds. Gradually, they've been fragmented and individualized, against identifying themselves with collective ethnic groups. It's not long ago when "whites" in America were recognized as a large variety of differing collectives with different, often conflicting interests, rather than as a monolithic group.
Italians, Irish, French, etc. have all been called names due to their ethnic background. But over time, they've chosen not to give a shit about it. Yes, an Italian will still get pissed off about being called names, but they're more likely to feel that insult in an individual sense rather than a collective sense.
If biracial people with a small amount of African heritage, want to keep fighting those mud-slinging racial battles, then by all means, keep doing it. But they'll be fighting those battles forever. You'll never be able to prevent people from insulting you by acting hurt, because hurting somebody is the precise reason why people insult others in the first place.
The only true way to delegitimize an insult, is to render it irrelevant. That's what the American whites have done. They don't care about being called rednecks, hillbillies, whatever. Some even choose to embrace that sarcastically.