I'm looking for advice on how to approach a friend and her mother on getting her male cat spayed

My friend current owns two cats, a female who was spayed after her fist litter and a male cat from that female who isn't spayed. Both are outdoors cats which I consider to be irresponsible considering there are a lot of stray cats near my friend's house, this of course has had a lot of consequences: the cats come back home scratched, bitten, with open wounds which have needed vet intervention and I have helped cover costs not to mention the risk of the cats being ran over or in an accident. (Not sure if I'm overreacting).

I told her that I'll cover the cost of having her cat spayed but she made some excuses (I can't it's my mother's cat she doesn't want to, I don't want him to loose his balls????) Then I asked why was her female spayed: -Because there are more (male) cats where I live(?) -And there aren't any (female) cats nearby? -No My guess is that the female was spayed because if she got pregnant it was THEIR problem, but if the male gets a female pregnant, why would they care?

I'm sure she thinks I'm being weird for thinking about her cat's balls but it just doesn't sit right with me, we ended up arguing and she said "Thanks but that's something you can't decide on" I'm looking for advice on how to re-approach this, I might be testing our friendship but I'm doing what I consider right. Also, if you think I'm overreacting, being insensitive or an AH about it let me know, opinions are welcomed.