Why do men do this sort of thing?
I think the vast majority of them who do shit like this are fully prepared to risk losing their children and are gambling on the fact the vast majority of women are not
The OP could call her partners bluff by saying that if he doesn't pay half for childcare she will walk out and let him sort out the entirety of childcare and she will have their child one night a week and every other weekend. But understandably she probably won't because she doesn't want to risk going through with it
But men like this, are fully prepared to risk having no/low contact with their children on the offchance it works and they can get what they want, which usually ends up being a full time parent to their child, housekeeper, someone they berate if they don't get sex when they want it, and someone they can financially control.
They know full well if they lose all contact with the child they will just use the 'my ex is a psycho bitch who took my children away from me and I can't afford to fight her' line, whilst doing their best to avoid paying child support
I'm pretty sure there would be a cross over in a Venn diagram with the other delightful subsection of men we hear about regularly on here who have unprotected sex and then if the woman gets pregnant 100% blame it on her as if she can somehow eject their sperm and actively chose not to