Didn't the student council president just resign because he is a 3rd year? They usually retire that year to go look for employment, and the 2nd year students replace them.

Ryuuen is having trouble deciding because Ayanokouji is too obvious a choice. He thinks it is a trap or a cover. Also, the other suspect isn't Yosuke, but Yukimura, who tied with Horikita at 100 (the perfect score) in the mini-test this episode, so he is technically capable of being a mastermind.