Men don't generally discourage other men from reproducing because it's just not effective. You can convince 20 men to not reproduce, and one that remains can still have 20 children.
But women discouraging other women from reproducing DOES work. And this is not just theoretical, the instinct is in fact real. Women are observed doing the following:
* Recommending bad haircuts to other women - studied and proven statistically significant
* Giving bad parenting advice which they would not do themselves - also studied and proven
The first example could be explained as mating competition, but the second is very clearly undermining reproduction.
Also while not formally studied, pretty much everything labeled as "feminism" can be explained as undermining reproduction.