Every bear in the game belongs to one of 5 affinities:
Particular matches in the game might favor a particular affinity. For example a particular match might double the Score Bonus of any Cautious bears used in the match.
School will service only one affinity of bear on a particular day. E.g., today may be a day when Merry bears can attend school and bears of other affinities cannot. Check the School Schedule to learn when a particular affinity gets to attend school.