Kyo watched from the sidelines as the other children picked their teammates. It was evident that no one wanted him on their team. They sensed his difference, even if they didn't know it.
Kyo realized he didn't want to be on a team; he'd rather be by himself. Martial arts were a perfect sport for him. It gave him an outlet to his frustration and anger over his curse and a chance to beat Yuki at something. He was able to practice by himself or spar with Kazuma if he wanted.
Teammates were not something Kyo needed -- neither were friends.