Au contraire. Birth rate dropped more from 1955 to 1965 (5.5 births per thousand), prior to the Sexual Revolution, than from 1965 to 1975 (4.5 births per thousand).
http://www.trinity.edu/mkearl/fam-kids.html
Drop in birth rates has been a continuing process since 1800. Here's a graphic.
http://lamarotte2.blogspot.com/2013/03/a-steady-drop-in-crude-birth-rate.html
No big change in the pattern can be seen in the 60s, coinciding with the sexual revolution, just a continuation of the drop, starting about 1955, that was a result of the end of the Baby Boom.
I agree in general with the author's POV, but wish he'd use accurate data to support his position, not just make stuff up.