Q: What do you call someone who is afraid of picnics?
A: A basket case!

Explanation: Picnics are relaxed, outdoor meals, often eaten on a blanket or a picnic table.  When you go on a picnic you take a picnic basket– a basket that has the food and plates and everything you need for the picnic.

“A basket case” is a term used for someone who has lost their mental health and is acting out of the normal (Basket Case is also a song by Green Day which I have never heard but will listen to now).  This joke plays on the term “basket case” because you bring a basket to a picnic and no one is really afraid of picnics… at least I don’t think they are.