Why are we so confident that women are the reason there are fewer children? In my circle nearly every woman has frozen or is freezing her eggs, surely that shows a desire to have children?
They want the option to have kids, at some yet-to-be-determined later time. It's St. Augustine: "please, God, make me good, but not just yet". I want kids, but not now.
They have also been sold the idea that having children by this method has a high success rate, when in reality it's of the order of one-third.
If I'm not mistaken, there have been 60+ million aborted preganancies in the US since the mid-70s. Pretty strong data supports the claim you are questioning, it's also probably the reason for recent successful attacks on abortion rights.