Russell's main argument is that the people we consider good are not actually good--they are just conventional. He begins with the example of Jeremy Bentham, a philosopher who defined goodness as doing good works. Bentham spearheaded many reforms, but was considered an evil man.
Russell discusses the attributes of a person who society considers "good." Such a person does not drink or smoke, speaks without foul language, and endorses the idea that we should punish sin. Such a person, Russell points out, can actually do harm, as he or she can defend the unfair treatment of others as condoned by God (as did the former Kaiser, a religious man). In addition, "good" people can often be pawns that start serious problems. He mentions, for example, Archduke Franz Ferdinand, who was murdered in Sarajevo--the spark that started World War I. As Russell writes, "the standards of 'goodness' which are generally recognized by public opinion are not those which are calculated to make the world a happier place." In addition, Russell cites several great thinkers, such as Darwin and Spinoza, who were known as bad men during their time, likely because they were unconventional. Russell says that our morality becomes superstition and that we need a new morality based on love of life and encouragement of growth.