I always thought it was a myth that men did not want children as much as women. They clearly benefit more, in pay, status, joy, plus don't have their bodies affected much, don't get mummy-tracked at work and don't have to do most of the slog (in the UK, different in some more gender equal countries).
I never really wanted children and when I moved here it was a hard no given the state of pregnancy care (you don't even get help at home after which you do in my home country), post-bird care, and work penalty. Many of my childfree friends say that they would have had children if they'd been male. I think young women are finally waking up to the reality, where men, as usual are lagging behind in their opinions.
The message needs to change to: being parents is an equal partnership, with both doing 50% (men doing bit more in the first few years to make up for the toll on women's bodies). And if that is not on the cards, well then no babies.
Women on this thread are a bit older and have now reached a point where they have the option of living without a man, and many find they prefer that. If men want o live with women, perhaps some introspection would be good on their part instead of telling us our views are invalid.