You've missed the main reason: children were always a pension mechanism, and today we have socialized (, and private) pensions. There's no need to have children if you think, in the end, the state (, or you bank account) will look after you.
* it's not the "state" that is supposed to look out for you, but your own money invested during the career. I see that money subtracted from my paycheck every month. I only want the state to provide stability and security so that money can be put to good use.