Hm, your question is so deep yet so brief that one wonders what is motivating it. But perhaps a brief question initially warrants just a brief answer. I imagine that racism is a position that holds (1) that (physical) race is a meaningful/legitimate category or way of classifying human beings and that (2) different qualities tend to be found in people of different races and that (3) some of these qualities are more valuable than others. Having stated it so baldly and so roughly it is NOT obvious why it is wrong; in fact it may well be correct (although actually proposition (1) is definitely a hard one to defend empirically, and proposition (2) is so statistical in nature, admitting of so many individual exceptions, that it is probably useful as a practical guide to behavior, if that is how people who endorse (10-(3) probably want to use it.) But of course what makes it "wrong" to most people is that it is (a) factually wrong (ie either one or more of those three propositions are false, or perhaps the specific qualities judged to be 'more/less valuable' are wrongly so judged) and (b) even if it's factually correct, the type of behavior it sanctions is morally objectionable for any number of reasons... (but details here would have to be worked out by looking at specific cases of alleged racism ....)
just some thoughts.