I think feminism is not the main cause of lower birth rates in Western countries, but the loss of purchasing power and increase of economic uncertainty about being fired or getting a salary cut.
The global balance is an incredible growth of human population, that puts in risk supply of food and other resources.
That's a very insightful way to look at it, you could however argue that decreased purchasing power comes at the price of women's liberation, which doubled the workforce and actually helped to drive wages down. Even many second wave feminist are distancing themselves from modern day feminism, which is increasingly telling.