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, while bears of other affinities would not get their Score Bonuses doubled.
School will service only one affinity 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.