That one ranks high on my list. If you're a farmer in the countryside children are an economic asset. They can feed the animals, plant, weed the crops, maintain fencing, etc. Once you move to the city, whatever else they are in terms of fulfillment, they're an economic liability.

Oddly enough, it's likely the US and Europe defused (and then some) Erlich's population bomb with farm subsidies which pushed people off farms and in to Nike factories in the developing world.

Is this still true when machines do the farming?

Not as much, but once you start mechanized farming you don't need many people in agriculture. There are few enough farmers in industrialized countries that they don't affect demographics much.

My sense is American farmers have more children than the population at large, but I don't have numbers to back it up. My farmer maternal great grandparents had 12 and 9 children -- I don't think that happens much anymore.

Yes, because you can let your kids use the machines at ages that would scandalize the urbanites (check the laws for your state, you find things like "twelve year olds can operate farm machinery incidentally on a road or highway").