In the December 2009 issue of the newsletter of the European Mathematical Society there is a very interesting interview with Pierre Cartier. In page 33, to the question

What was the ontological status of categories for Grothendieck?

he responds

Nowadays, one of the most interesting points in mathematics is that, although all categorical reasonings are formally contradictory, we use them and we never make a mistake.

Could someone explain what this actually means? (Please feel free to retag.)