ah.. yes that part.. I think or well Naoto wasn't against the idea of having minato but the thing or main issue was that Hazuki was still in college and knowing Naoto's personality he definitely didn't want to burden him further with another child as it's quite expensive. I believe he wasn't against the idea as he himself mentioned that "if we have a kid" and was rather reluctant because he was afraid to burden Hazuki further.
Spoilers but a question...
Someone please explain to me how the middle childs conception was consensual because its ruining the whole vibe for me feeling like the alpha forced that after knowing everything about the ukes past.