It is round 2 of a 6-player game, so 3 players are needed for the mission. Alice (loyal) is the leader and strongly (but silently) suspects Bob of being a traitor, perhaps due to a "tell". Carol also suspects Bob and is strongly saying so, and Bob is playing offended.
Alice nominates all three of herself, Bob, and Carol for the mission. She knows that Carol will vote no and will vote no herself, so if even one other member is skeptical the vote will fail. Meanwhile, Alice carefully watches the votes from Donald, Elaine, and Frank. A yes vote, especially a single yes vote, is a suggestion that one of those players is a co-spy; not an ironclad proof, but a possibly-important hint.
Same situation, but in this game Alice is a spy. Carol's suspicions about Bob are baseless. Alice still goes through the motions of this charade even though Bob and Carol are both loyal, to throw off suspicion that would arise because she is not going through her typical plan.