These viruses take over the cells in your nose and throat and use them to produce more viruses. After a few days, your immune system notices and destroys it,3 but not before you infect, on average, one other person.4 After you fight off the infection, you are immune to that particular rhinovirus strain—an immunity that lasts for years.
If Sarah put us all in quarantine, the cold viruses we carry would have no fresh hosts to run to.