>>> nan = float('nan')
>>> min(nan, 5)
nan
>>> min(5, nan)
5

Good arguments can be made in favor of either result, but different value for min(x, y) depending on the order of arguments can hardly be justified.

"In the face of ambiguity, refuse the temptation to guess" suggests that min/max with NaN should be an error.  See also issue 11949.