The reason for this is that Thomas Jefferson was a democrat. He believed that the government should be in the hands of the mass of common people. In order that those people should be better able to handle this task, he believed in a system of universal education.
Jefferson believed that all people were capable of participating in a democracy, particularly if they were educated. He felt (unlike people like Alexander Hamilton) that big decisions were not beyond the common people. To him, the ideal country was one in which all people were relatively equal, were mostly small farmers, and had enough education to participate in government. To achieve this ideal nation, he wanted to establish a system of public education for all Americans.