Disclaimer:Naruto isn't mine
Being a dad means gently telling your wife to push while she's shrieking for you to shut the hell up. True bonding.
Little known fact about Naruto: As brave and strong the Hokage was, Naruto had an intense fear of his stomach being cut open or cut off. You could cut off his arm, neck, head, legs but nothing would make him suffer more nightmares than his stomach. Sasuke wanted to know if it was possible to have your stomach cut off. That is why, Naruto begged and pleaded, and got into serious debates(all with himself) about whether he should the deliver the baby in his Sexy No Justu form. The baby would still be his, wouldn't it? Or would it be the infamous Naruko's.
Sasuke offered his advice, that he had gotten Naruto pregnant and not Naruko. It would only make sense that Naruto was the one who delivered the baby, even if Naruto was scared to death at the prospect of being cut open. In the end, Naruto did what was best.
He asked to be thoroughly put under anesthesia and knocked out before heading for the C-section.