Badminton is big in Asia and has a lot of countries participation in the World Championships, not like baseball which is big in a select few countries and basically non-existent in the rest of the world. They dropped baseball and softball because of the "must be present in a lot of countries"-requirement. If they had two drop some more, badminton would not be the first to go.
I really think this argument is ridiculous. The sport is huge in Cuba, Venezuela, Dominican Republic, Japan, the U.S., Taiwan, and South Korea. Plus it's popular enough to field competitive teams in Mexico, Canada and others. There are several sports in the Olympics where there's not this global reach and popularity, it's not like American football which is only popular in the U.S. The truth is that it's just not popular in Europe, and Europeans have dominated the leadership at the IOC so they decided to get rid of it.