It does, however, make the mystery even more surprising because it notes that eel was plentiful in the New World, and was a critically important food for the early colonists. They were taught to catch eel by the native American Tisquantum (AKA Squanto), the Patuxet man who had been kidnapped by an Englishman and taken to Europe. After nearly being sold into servitude and suffering humiliations in England, he finally managed to get back to his country only to find that his people had been wiped out by disease. He was living with the neighboring Wampoanog when he met the Pilgrims, and taught them to catch eel, plant corn, etc. He was very generous, and is considered essential to the Plymouth colony's survival (even with his help, half the colony died within the first six months).
The book makes it clear that eel were plentiful and popular as food. Even in 1880, 400,000 lbs of eel were captured commercially in Massachusetts, but about a hundred years later, in 1988, it was down to only 29,900 lbs, and in 1997, only 304 lbs were caught (p. 120). A big drop-off in consumption occurred after WWII, with only ethnics (Italians, Poles, and Irish) eating eel. The book suggests that this is due to eels being bottom feeders, so that they concentrate heavy metals and pollution. Indeed, eating fish from the Hudson River of New York was banned in 1976, especially eel, when it was discovered that the PCBs released by a GE plant had poisoned about half the eel in the river. This still does not explain why so many Americans are grossed out by eel, though. There are many things we don't eat that don't generate the disgusted comments on websites that explain how to cook eel.
While looking up recipes for eel, I discovered this entry at the start of HowStuffWork's entry on "Why are eels slippery?":
One of the creepiest animals you can encounter in the water is the eel. It's a slippery, slimy creature, and it doesn't fit neatly into the water creature categories we've set up in our brains, which only amplifies our fear of it. Is it a snake? A fish? An unholy hybrid of both?
To anyone who has read Mary Douglas, this explains everything. Americans do not consider eel to be "clean" and edible not because it is a bottom feeder (so are crabs and lobsters, after all), but because it does not fit into a proper category. It is actually a fish, but it looks like a snake. It can even live a long time out of the water. Plus, it does not die right away and continues wriggling, adding to our fear of it, especially for those of us who are not used to killing our own food (we Americans expect that to be done by immigrants in slaughter houses, so they can remove the heads and tails of fish so we are not reminded that they are real animals!).
This still leaves the question of why there has been this shift since WWII. Surely American categories have not changed during the 20th century. Why has this become more salient? Why did a favorite dish of the early 19th century disappear from cookbooks of the 20th century?