population rates go down when women have more rights and education

Less pirates means more global warming, so if you are against global warming, you are supporting killing innocent sailors.

But seriously, the reason is that for subsistence farmers more kids meant more available labour and it increased their quality of life. That was the primary reason for high birth rates. For industrial/office/service workers more kids inevitably mean a lower quality of life, and increasing atomization of society and economic troubles just make this fall sharper. In fact, you can look at historical data and see that urban birth rates were always god awful (usually even lower than present-day) and it was rural areas that provided cities with people. With urbanization and replacing subsistence farming with industrial farming this source has been destroyed. The right wing can destroy women's rights, but it will not bring birth rates back. In fact, in will result in less available labour for industry and fall in the quality of life, which will result in lower birth rates.