USC Trojans:

So why does USC name its team after losers? And not only that, but why did the Trojans lose? Because they were dumb and gullible. What kind of mascot is that?

UPDATE: USC lawprof Howard Gillman points to this explanation (emphasis added):

Originally, the teams of the University of Southern California were referred to as Methodists or Wesleyans, names not favored by university officials. The director of athletics, Warren Bovard, son of university president Dr. George Bovard, asked Owen Bird, a sportswriter for the LA Times, to give the university a new nickname. Although we now are proud of a winning tradition, the USC family was not always successful during the early years. In fact, we were named "Trojans" because we were great losers. Bird dubbed the USC team "Trojans" instead of "Methodists" because he compared our players in 1912 to noble Trojan warriors. His reasons for using the term were that "At this time, the athletes and coaches of the university were under terrific handicaps. They were facing teams that were bigger and better-equipped, yet they had splendid fighting spirit. The name 'Trojans' fitted them. ... I came out with an article prior to a showdown between USC and Stanford in which I called attention the fighting spirit of USC athletes and named them 'Trojan' all the time, and it stuck. ... The term 'Trojan' as applied to USC means to me that no matter what the situation, what the odds or what the conditions, the completion must be carried on to the end and those who strive must give all the have and never be weary in doing so." ...
So they admit it! But I agree that the USC Methodists would be an even odder name for a football team.

FURTHER UPDATE: The Llama Butchers (?) comments: "Two! Four! Six! Eight! Who Got Tricked And Opened Their Gate?"