What does the movie "Who's Afraid of Virginia Woolf" have to do with the author Virginia Woolf?

Answer 1

Two reasons, I'd say:

1. Because Ms Woolf wrote almost exclusively about very troubled relationships and the many ways that people can and do hurt one another, the "games" people play.

2. Well, because of the pun - Who's afraid of the Big Bad Wolf - from the Disney cartoon about The Three Little Pigs:
"Who’s afraid of the big bad wolf,
big bad wolf, big bad wolf,
Who’s afraid of the big bad wolf?
Tra la la la la.
Who’s afraid of the big bad wolf,
big bad wolf, big bad wolf,
Who’s afraid of the big bad wolf?
Tra la la la la."

Answer 2

The two men characters are professors at a liberal arts college. One cracks a joke when one couple is visiting another at home, which is a take-off on the children's song, "Who's Afraid of the Big Bad Wolf?" The point of the joke is to show the audience how precious and rarefied these characters' lives are that they make jokes about esoteric literature.