Mac version of man doesn't have the -u option. How could I rebuild man's database of commands?
The man command actually doesn't have a database of commands except when mimicking apropos with the -k command. The -u option in Gnu man just checks the cache used by man to speed up some lookups.

The only database is the whatis database. It is used by  the whatis and apropos commands. It can be created or recreated by the makewhatis command - sudo /usr/libexec/makewhatis.