SQL Booleans vs ManyToMany
One problem with using a boolean column for each tag is that you would be limited to two tags only.  If you ever want to support tags for breaststroke, butterfly, sidestroke, doggy style, … those would all require schema changes.  You would also have to alter your queries to support those columns.  As a result, your application code won't support tags in general; each tag will feel like a new feature that you have to add code for.

(MySQL has no true boolean type.  The closest approximation would be numeric types TINYINT(1) or BIT(1).)