On page 173 of Paolo Aluffi's Algebra: Chapter 0 he says:
Fiber diagrams are commutative, but "even better" than commutative.
What is he referring to when he makes the statement that they are even better than commutative? The only thing I can think of is that these types of diagrams have a universal property, though I don't see why this property would be emphasized with a square in the center of the diagram to denote it. Is this what he means, or is there something else special about diagrams?