What’s funny about watching someone struggle with an unruly umbrella? Few, if any, have come up with a better explanation than W H Auden who took a stab at it in 1952, and came up with two reasons :
“a) An umbrella is a mechanism designed by man to function in a particular manner, and its existence and effectiveness as a protection depend upon man’s understanding of physical laws. An umbrella turning inside out is funnier than a hat blowing off because an umbrella is made to be opened, to change its shape when its owner wills. It now continues to change its shape, in obedience to the same laws, but against his will.
b) The activating agent, the wind, is invisible, so the cause of the umbrella turning inside out appears to lie in the umbrella itself. It is not particularly funny if a tile falls and makes a hole in the umbrella, because the cause is visibly natural.”
See: ‘Notes on the Comic’, Thought: Fordham University Quarterly, Volume 27, Issue 1, Spring 1952. Also re-published in ‘The Dyer’s Hand : and other essays’, 1962
BONUS assignment [optional] Have you got a better explanation?