I don’t see how that has anything to do with forcing a private institution into serving customers it doesn’t want to.

The argument is: Imagine you and a friend have a private tutoring business. You should be able to have the freedom to pick whatever customers you want, your not a slave, your not obligated to provide a service for someone if you don't want to. Over time if there is demand for private tutoring that you and your friend aren't willing to meet, there will be others who will provide that service because there is profit in it.