Children are massively more expensive, and less useful, in richer societies. I don't think anybody in Japan would be allowed to provide for their children the standards of care provided in a country with a growing population. As for the second point, if you are a farmer in a country with little physical mobility, your children are your retirement savings. If you live in America, your children are future employees of a company ten states away.
I read a statistic somewhere that it costs $2M to raise a child. Considering that it's considered a horrible imposition to ask your kids for money, or even to ask them to take care of you, it's easy to explain why urbanization, industrial development, and education, work against population growth.