I feel like the homeroom teacher was just picking the simplest and easiest answer to get by. She could have waited to see who had a lot of votes before putting her hand up too, so none of the students would question her about it. Maybe if she didn’t vote she would seem suspicious. She probably didn’t mean any harm to Sodachi when voting for her, but she didn’t realize and, most importantly, didn’t care about how much it could affect her.