If the Infected Person is wearing the mask, all good. Cough contained in mask, no virus spread anywhere, everyone OK.
If the Non-Infected Person is wearing the mask, they're still covered in virus-laden cough mess. All they have to do is touch their face once in the next 3 days to catch the virus. Washing their hands will remove the virus from the hands, but not from their clothes, hair, etc.
Also, they're now covered in virus. Everything they touch will be covered in virus. Virus everywhere, infecting everyone. Everyone not OK.
It's possible that a non-infected person wearing a mask might prevent a tiny bit of infection, but it's MASSIVELY more effective on the infected person.
Surgeons wear masks in case they cough on the patient. They don't put a mask on the patient...