In this interpretation we expect decision-makers to be utility-maximizers - for example, as whether I buy or not Thing X; so, we expect Gumbel (an extreme value distribution) errors. But we're looking for Utility(1) minus Utility(0) (buying vs. not buying) and the difference between two Gumbels is a logistic.

More detail: http://fisher.osu.edu/~schroeder.9/AMIS900/ch5.pdf