crt is a subset of a broader critical legal theory. the idea of critical legal theory is that the law is just a tool to push through political opinions, so all this idea of reasonable people and objective rational logic is just a lot of bullshit - smoke and mirrors to cover the state's application of it's ideological aims. it applies to all kinds of things. crt is a racial application of the broader theory to the remnants of apartheid in the american south.
the way i'd explain it quickly in a youtube comment is just that the official approach to legal theory has it backwards. the basis of our legal system is that the judge is supposed to look at the evidence and draw a rational, logical conclusion of how the law applies to it, in a way that is consistent with existing legal precedents. what the critical theorists says is that this is, in practice, almost always just a utopian abstraction. what judges actually do is form an opinion, then go looking for a precedent that backs up the opinion. there are so many legal cases to draw upon that this is more or less a worthless formality, especially at the higher levels. the court system consequently reduces to a person in a robe enforcing a subjective and personal opinion, not an objective system of impartial justice. justice is not blind, but merely the personal opinion of the judge.
i wouldn't consider this to be radical. it's pretty apparent, actually, if you take a look through some case law. and the applications are very, very wide.
now, a lot of things are going to affect those personal opinions. crt is just the idea that racism is going to be one of them, if the society is rooted in racist institutions. and, through large swaths of the southern united states, this is pretty apparently true.
now, soledad is right in pointing out that you're going to read this at any school. not just harvard. it's in the spectrum. it can't be ignored. teaching it doesn't imply any partiality towards it. it's just barack doing his job.
but, suggesting that it has nothing to do with white supremacy is disingenuous. it is the basic premise. but, it's not particularly radical to acknowledge that it's an accurate premise - so long as you're careful about your application of it.