Actually, vaccinated people can infect others, as vaccines are not 100% and in fact, vaccines can mask the symptoms. Example, pertussis (whooping cough) vaccine can cause asymptomatic carriers (remember "Typhoid Mary"?). Personally, I'd rather that somebody who has pertussis, stay home because they know they are sick because they have symptoms, than have them think they are healthy and spread pertussis because "I had the vaccine so I'm healthy".

Sources:
https://wwwnc.cdc.gov/eid/article/6/5/00-0512_article

https://well.blogs.nytimes.com/2015/06/29/symptom-free-carriers-may-be-spreading-whooping-cough/