F. Scott Fitzgerald's "Nor Does He Spin" subheading title, what does he mean by spinning?

"Neither does he spin" is a way of saying that Anthony Patch "does not toil", that he does not do any work.

A familiar reference to many people older than about 50, I think. It refers to a passage in the Christian Bible, Matthew chapter 6, verse 28:

Why are you anxious about clothing? Consider the lilies of the field, how they grow. They don’t toil, neither do they spin.

Wikipedia commentary: Two verses earlier at Matthew 6:26 Jesus told his followers not to worry about food, because even the birds are provided for by God. In this verse Jesus presents the example of the lilies, who also do no labour. Spin in this verse is a reference to spinning thread, a labour-intensive but necessary part of making clothing. Spinning was traditionally women's work, something made explicit in Luke's version of this verse. This then is one of the few pieces of evidence that Jesus' message is meant equally for women as for men.