"I married him because I thought he was a gentleman," she said finally. "I thought he knew something about breeding, but he wasn't fit to lick my shoe." (Chapter 2)
Considered in context, the quotation takes on contextual sense but Myrtle exposes her own lack of "breeding" by the way she phrases her remark, which adds to the difficulty in understanding it.
- 6. breeding: to develop by training or education; bring up; rear: He was born and bred a gentleman. (Random House Dictionary)
What Myrtle is literally saying is that she thought Wilson knew about how to propagate offspring: 1. Breeding: to produce (offspring); procreate; engender (Random House). If you know something about breeding, you know how to do it: "I thought he knew something about breeding."
What Myrtle really means is that she thought Wilson was himself well-bred, as in the sense of meaning number 6 (above): to be developed in gentlemanly ways through training and education as part of one's upbringing (or ladylike ways).
This makes sense with the context and, conversely, this is the one meaning that gives sense to the context. Myrtle thought Wilson was a gentleman, one who was bred by training and education to be courteous, gracious, large-minded and, in Myrtle's eyes, able to provide financially:
He borrowed somebody's best suit to get married in and ... I lay down and cried to beat the band all afternoon.
However, Myrtle finds out that owning his own garage makes Wilson neither courteous nor financially successful, thus her complaint that she thought he had been a gentleman and that he had been well raised, instructed and educated. She should have said:"I thought he had breeding," not "he knew something about breeding" since the phrasing creates two entirely different concepts. Her mistake in speaking adds to Fitzgerald's characterization of her: she is not intelligent and had not had good breeding herself.