So, if you were a woman, would you willing submit to any control over your ability to get an abortion? I would suspect not.
I see the point of this article as a way to engage women in a discussion about inequity in gender roles. I agree with you that the trend towards blaming men for every ill has gone too far when the real culprit is the general structure of our societies. It can be very difficult to get women to consider rejecting traditional expectations in their favor when they are just now finding ways to push back against the traditional expectations that are not in their favor. An analogy would be granting freedom to a slave, but only within the confines of a totalitarian state where she is still enslaved compared to a free society.
Most women want to hear about how they should be freed from patriarchy. They are less inclined, though, to want to hear about how men should be freed from patriarchy as well.