Wearing a mask protects other people as well as ourselves.  People can be spreading the virus even though they feel well.  You can't develop herd immunity until 60% of people have been exposed, and until we have better treatments that is too risky to try to attempt -- too many people will die or develop long-lasting side effects.  We have to wait until there is a vaccine or a reliable treatment.  Clearly we cannot rely on citizens to do the right thing, so masks must be mandated in indoor public spaces.   We have lots of safety mandates that people follow (seat belts, smoking regulations).  Government also enforces regulations that not everyone agrees with (women cannot go topless on the beach, for example) that are deemed to be "in the public interest".  This is no different, and is crucial in protecting the public health.