"Opposite extremes" are places that are far from each other. They are the farthest possible from each other. On a map of Africa, South Africa is farthest south, Tunisia is farthest north. Measured by latitude, South Africa and Tunisia are at opposite extremes. El Azizia in Libya is the hottest place in the world. Antarctica is the coldest place in the world. With respect to temperature, Libya and Antarctica are at opposite extremes. Figuratively, ideas that are very different could be "at opposite extremes." One might say "The ideas of economists Keynes and Hayek were at opposite extremes." I find from a web search that your quotation is from "Guns, Germs and Steel," by Jared Diamond. The full passage is "Some readers may feel that I am going to the opposite extreme from conventional histories, by devoting too little space to western Eurasia at the expense of other parts of the world." What he means here is "conventional histories devote too much space to western Eurasia. Some readers may feel that I am devoting too little space." Exaggerating, if conventional histories were entirely about western Eurasia, and if his book said nothing at all about western Eurasia, then they would truly be at opposite extremes. (By the way, he actually made a mistake--he didn't mean to say "at the expense of.")

Most people agree that sometimes it is OK to yell, and sometimes it is not OK to yell. Some people say it is never OK to yell, and other people go to the opposite extreme and say it is never OK to yell. I'm not sure which extreme "conventional histories" histories are seen as taking in this passage, but maybe it is the extreme view that old white men are more important than other people. If so: "Logically, every group of people should have about the same importance in history. Conventional histories focus mostly on old white men, and imply that they are better or more important than anyone else. Some modern histories go to the opposite extreme, and imply that old white men are universally evil or irrelevant. Good scholarship should avoid both extremes."

be at the opposite extreme means that you write something completly different, the opposite ftom them.