Can similar charges attract each other?

Your teacher might be referring to this article:

Ball (2012), Nature News: Like attracts like?

The key to Lekner’s seemingly bizarre conclusion is that the spheres are electrically conducting. This means that charge can get redistributed non-uniformly on their surfaces. ... When far enough apart, the two spheres do act like more-or-less uniformly charged objects, which repel one another when the charges are alike. But as they get closer, they become polarized: one sphere elicits an image charge in the other by pushing like charge away. At close enough range, the resulting attraction wins out.

If you got point chargers, then there are no way two electrical chargers with the same sign attract each other. But if you do not have point chargers but charged bodies (I mean that have volume), each body will have both positive and negative chargers, but if the body is not electrically neutral it will have more of one of the two types of charge. The charge can move inside the body and because of this you can create a separation of charges if you approach one electrically charged body to another. This is for example the principle of charging by Induction.