They founded it because Williams felt like Massachusetts did not own land because they did not by it from the native, so the colony of Massachusetts threw him out and he fled to Rhode Island and founded Providence, Rhode Island.
Anne Hutchinson helped found Rhode Island as well. She got thrown out of Massachusetts because she thought that you don't have to pray and do good. She thought that the faith was enough. 2 years after Providence, Rhode Island was founded she came and helped found Portsmouth, Rhode Island.