This is a double standard. Why can Eve be allowed but other women not?
I don't see how it's a double standard. Up to the birth of Jesus, mankind had to bear children so that Jesus could eventually be born. Jesus was already born, so the childbearing that was needed to bring forth the promised seed is complete. So in that interpretation, Eve and her descendants that would all be progenitors of Jesus are the ones who were literally "saved through (their) childbearing" (not apart from faith- but in the same way that Noah was "saved through water") it was the
method of their (and our) deliverance.
So, I think he is using Eve as an proto-type for women in this instance in order to say something like...
"Eve still had a role to play in God's plan of deliverance for mankind, despite the fact that she was deceived" and like Eve still had a role, women in general have a role to play in God's plan of deliverance today.
Just through observation of people, I can look and see that childbearing has no definite effect on women's attitudes toward God, AND I really don't like how a "church" could potentially use this verse to try and coerce women into marriage and pregnancy... I really don't believe that is what this verse is for, or referring to.
Granted, I have not word-nuked this scripture, maybe I am wrong- but I would suggest that before you make a major decision based on this scripture, to take a deeper dive than just a surface level examination of the text and PRAY. ALOT.