… The argument goes something like this. Racism is a system in which one group of people exercises unjust power to the disadvantage of another group of people. Part of the way such a system survives is by reinforcement, by enough people continually affirming that the system is the way things should be.
Now, the fact is that, all things being equal, you’re better off in your country and mine if you’re born white. There is a (gradually diminishing) system in place that works to the continual disadvantage of black people. Now consider Howard Cosell (I believe it was) talking about how blacks are better athletes because slavery weeded out all but the strong. That reinforces the dominant system of power because of the implicit “… and also weeded out the independent, the ambitious, the smart.”
Now consider the slogan “white men can’t jump”. That’s almost the reverse: saying that whites’ genetic heritage just makes them inherently bad basketball players. Suppose everyone believed that - would that materially change the distribution of advantage and power? (Would it make you decide that it would be better to be born black?)
If you are concerned with a more equitable society, you might see it important to distinguish between prejudices that maintain inequality-based-on-race and prejudices that are irrelevant to that.
That’s not to say that a white individual couldn’t be harmed by the prejudice of a black (or asian or whatever) individual. It’s just to say that, while individual prejudices (white against black, black against white) may look the same, they have different effects when all summed together.
That, as I understand it, is what is meant by the unfortunate sound-bite “blacks can’t be racist”. It sounds - and is - silly if you think “racist” is a synonym for “prejudiced”. But the sound-bite-utterers don’t think it is (at least, some non-silly ones don’t).
It’s certainly arguable that using the charged word “racist” in a subtle way is a bad idea, but what’s done is done.