A positive externality exists when people who are not part of an economic transaction gain benefits from that transaction.  A person attending college definitely creates positive externalities for the society as a whole.

If a person goes to college and society does not pay for it, positive externalities arise.  By going to college, the person increases their human capital.  They come to be able to do jobs that will benefit society.  They may become a teacher and help the next generation of children learn or they may become a scientist and discover a new medicine that will benefit society.  If these (or any one of millions of other things) happen, society gains without having paid for the person's education.

In this sense, college education can create positive externalities.  It therefore would make sense that it should be supported with taxpayer money.