The idea that men don't want kids it's all women is one that is deeply embedded in society, and one that is constantly reinforced in loads of films TV progs etc.
That's not what I see in real life though. Plenty of men want children and love them and are hands on etc.
If men REALLY didn't generally want children then surely there is loads they can do-
An effective contraception method for men that is reliable etc eg a pill, jab or similar. So they can be more in control of fertility.
Be in favour of easy access for women to contraception, MAP and abortion. Obv not saying that those aren't women's choice. However if men don't want children, then it's obviously nonsensical to restrict/ ban access. Generally the objections, while plenty of women support, are from patriarchal values and religions. Men could alter this globally. Might be slow but could be done as men tend to have the majority/ all of the power in govt etc.
And maybe. To work to disseminate a shift in what's seen as sex, usually PIV is what 'counts' (now anal of course which is not at all good for women/girls). Pushing the fact that there are plenty of other ways to share sexual pleasure, and come with essentially zero risk of pregnancy. This would benefit everyone for a number of reasons. Don't know if it would get far! But has been talked about for a long time.
Maybe some more things?
The fact is that if men don't want children there is plenty they can do, or could work towards, to lessen the risk.
I mentioned earlier though that plenty of men do want children. Esp male children in many parts of the world.