Gyutaro emerging from Daki's body to fight Tengen Uzui was easily the biggest surprise in Demon Slayer: Kimetsu no Yaiba's "Entertainment District" arc. Tengen knew instantly that Daki was far too weak to be the demon he was searching for, let alone an Upper-Rank, but even he was caught off guard by Gyutaro's creepy and grotesque entrance. Though it quickly became clear that Gyutaro was the true Upper-Rank Six, what was never clarified is why he was inside Daki's body in the first place.
When Gyutaro and Daki were human, and her name was Ume, they were siblings who lived in poverty until Gyutaro discovered his fighting skill and Ume began getting attention for her beauty. Ume has never had any shame about calling on her big brother to ride to her rescue, and it's a job Gyutaro is very proud to have. He thought of her as his pride and joy and was devastated when she was burned alive while he was away. Once they became demons, apparently Gyutaro discovered a way to never have to risk being apart from Ume again.
When Gyutaro and Ume were found by the former Upper-Rank Six and turned into demons, their lives became permanently intertwined. Daki can't be killed when Gyutaro is inside her body, and when he leaves it, neither one of them can be killed unless they are decapitated simultaneously. Although, Tengen Uzui suspected that if Gyutaro were to absorb Daki and then be decapitated, they would die -- which Gyutaro did not refute. As Daki was much closer to death than Gyutaro when they were turned into demons, it seems he became the main unit of the two.
Gyutaro's ability to exist inside Daki's body apparently isn’t just so they never have to be apart, but it's also the safest state of being for her. Keeping his sister safe is Gyutaro's only goal in life, so he seemed content to just stay inside her body and let her do as she pleased until she needed him. Even when Gyutaro is forced to leave Daki's body to defend her, he still looks after her above all else. Gyutaro even went as far as giving Daki one of his eyes to power her up, but also so he could literally keep an eye on her while they fought separately.
Gyutaro claimed to Tengen that he and Daki are two people in one, and it became clear he didn't only mean their power and status as Upper Six, but their bond. When they were kids, Ume was the light of Gyutaro's life; having such a pretty sister ended his own inferiority complex and he became proud of his ugly appearance. Keeping each other warm during winter, Gyutaro promised Daki that they would never be apart. His pledge held true into the afterlife as a child version of Ume chose to accompany Gyutaro to Hell rather than go into the light without him.
Even Demon Slayer protagonist Tanjiro Kamado noticed the eerie similarity between his bond with Nezuko and Gyutaro's and Daki's relationship. As siblings who love each other more than anything in the world, there's nothing Gyutaro wouldn't do for Daki. Just as Tanjiro refused to let Nezuko be killed for being a demon, Gyutaro refused to let Ume die. And if giving up his own life to exist inside Daki's body keeps her safe, Gyutaro had no issue lying dormant while his sister lived the life he felt she should have always had.
