First off, John seems to see himself as the victim of a conspiracy of females to either physically or socially castrate him and this leave him the helpless victim of ridicule and abuse. Rather than admit that he's a callous, abusive oaf who can't care about anyone who ain't him, he bleats about people wanting to neuter him because they're crazy and wrong. He'd probably prove that by asking Elly to go through the painful and intrusive step of having her tubes tied so that he wouldn't have to endure day surgery.
Secondly, Elly seems to be obsessed with the idea that given half a chance, a man is going to cheat on her. We don't know a Hell of a lot about her teenaged years but it seems to me that she'd made more of a relationship with some boy she had a thing for than he did. The trauma of being told "I'm just not that into you" seems to have been so great that fearing the jeering of the uncaring, she fled her home and didn't stop until she got to Toronto. This means that she's gotta think that if he doesn't want to be neutered, he must want to bang his harem.
Third, we have to deal with the fact that both of them fear and hate the idea that their children know things that they don't feel comfortable talking about. If they can keep them ignorant, they don't have to face uncomfortable conversations and don't have to worry about their children being truly autonomous adults.
The result would be progressive and ground-breaking but for all the wrong reasons....just like the Housening and Settlepocalypse.