I don't buy the 'some men find babies boring when they're little and he will probably be better when the baby is older'.
Lots of people find babies boring, me included. When I had a baby did I enjoy doing baby yoga, singing nursery rhymes, playing peekaboo, looking at the same picture books, building towers and helping them knock them over? Not at all and I'd have much rather just sat on my phone all day. It didn't come naturally to me at all, but I did it, because I'm not a lazy twat and I didn't want my baby to be starved of any interaction and not develop normally, which is essentially what would happen if they were just plonked infront of the tv the whole time. 3 months is old enough to get some smiles and interaction so the 'boring baby' argument doesn't really hold up anyway but my point is it doesn't matter if he finds it boring he still has a responsibility to parent her, and that involves a level of interaction.
Also plenty of men leave all the parenting of older children to the mum because they've consistently checked out so the baby ends up only wanting the mum. And plenty of men with older kids effectively ignore them and sit on their phones all day.
My point is I dont think it's acceptable that he is being a shit parent because it's boring. If parents got to check out of the shit boring bits of parenting they wouldbt be there when their child was sick, needed to practice anything, needs driving places etc etc
Its shit that he called you a nag as well. (I'm assuming you approached it fairly ie saying something about his actions and how it made you feel, such as 'I've seen you've not spoken to the baby all evening, I'm worried you're not bonding' rather than taken a 'you're a shit dad's approach). You're raising a valid concern with him and it does affect you - if he doesnt interact with the baby that means you automatically have to be the one that does all the talking / singing / games etc. and probably feel like you can't have an off day and plonk her infront of the tv for a bit as she will be getting that with her dad later. It's also hurtful if you feel like you have to ask someone to spend time with you and that they would rather be doing something else.
I'm not sure what the answer is though. You can't really change the way someone feels or acts. You can only really tell him how it makes you feel and have boundaries about his behaviour such as moving out if it becomes unacceptable