Why does every criticism of China have to have a corollary accompanying US criticism? Can we not just talk about one issue at a time instead of muddling up the waters?
In an ideal world, everyone criticizes things they know the most about and can do the most about, which is whatever is happening in their own country. When this is inverted, there is usually some ulterior psychological need and the criticism ends up not being anything genuine or actionable but a pissing contest. Anything goes in a pissing contest. Why are you surprised?
Use of the phrases like these, exemplifying the tu quoque logical fallacy, was an attempt to deflect criticism of the Soviet Union by referring to racial discrimination and lynching in the United States.
Look at it from the other angle. If you are to blame someone for doing XYZ I assume that you are sparkling clean. If however you are doing the same thing simply get lost. You have no moral right to blame someone for doing exactly the same thing you do.
It is not "Classic Chinese / Soviet tactic (TM)". It is a friggin natural sense of justice that normal people possess.