It's a factor, it's not the only factor.
Decrease in teenage pregnancies, decrease in alcohol consumption, contraception and day after pills, higher levels of education, less socialized culture, less generational housing etc.
Having a child is more than often a deliberate, calculated decision that is made by adults whereas in the old world pregnancies happened left and right with little to say about it. Support systems existed because the problem was pervasive. Now the problem is generally gone, and the support systems thereafter.
No country has managed to reverse the trend of declining birth rates. The better quality of life people have, the fewer children people tend to have.
It's not just about who does and who doesn't have children, it's also how many children per family. 1-2 children is the new normal. My grandpa was #7.