Izumo didn't do intimacy.
She was a distant person by nature, even as a child; even before her mother hated her, before she learned to rely on nobody but herself as her mother stopped coming home in favor of her treasured Sō-sama, before the illuminati made her cursed mother into a lab rat and tore Tsukumo away from her- even before she was made into the distrustful, hateful person she was, Izumo had been distant to everyone but her beloved little sister and later Paku.
Distance was both safer and easier; people couldn't hurt her, use her, or betray her if she never let them get close enough to do so, after all, the notion becoming even more engraved in her after the illuminati ripped everything she held dear away from her, after they used Tsukumo against her to get her to obey them, all because she stupidly, stupidly trusted them enough to ask for their help. To Izumo, things like trust, relying on others and the vulnerability required for intimacy weren't simply stupid- they were dangerous things that could easily put her in a helpless situation once again, the prospect more terrifying than any demon Izumo could ever face. Keeping her distance from others and closing herself off to any sort of intimacy, be it emotional or physical, kept her safe- so that's what she did for years and years, never letting anyone but Paku close under any circumstances. It was scary idiotic to willingly give someone the power to hurt you by allowing them to get close to you, anyways. What kind of idiot someone a knife and turns their back to them in hopes that they won't stab it deep into their spine, anyways?
Moriyama Shiemi was, in every shape and form, an idiot.
She was the most gullible, naïve and loving eager to please person Izumo had ever met; a shut-in out into the crapsack of a world for the first time, someone desperate to make friends and be helpful to everyone. She'd barged into Izumo's life, eager to be friends with her- her honesty and trusting nature, or more accurately, the fact that the girl was able to be this way, to wear her heart on her sleeve, filled Izumo with envy and bitterness to the brim, and it was all too easy to use her naivety to manipulate and use her like a servant under the guise of friendship. At first, Izumo did not see her as a friend, and she didn't care about her or whether she was hurting her- it was Shiemi's own fault she was letting Izumo boss her around, and if she didn't like it, Izumo was not stopping her from standing up for herself. In a twisted, ugly way, Izumo wanted to "help" the trusting, innocent, gullible girl by being the one to open her eyes to the truth of the world Izumo had learned the harsh way: that people were selfish, horrible creatures, and that trusting them would only lead to getting hurt one way or another. Feeling foolish and upset that someone manipulated you into doing chores for them was better than hating yourself for inviting a monster to destroy your family and ruin your life with a pay phone and a business card, after all.
Ironically, however, Izumo was the one who ended up changing because of Shiemi, rather than the other way around.
As Shiem ventured into the world, experiencing and seeing more of it every day, going through ugly, jarring things no average person let alone a former shut-in like the girl would live, as she grew with experience, blossomed and bloomed from the seed she used to be, she did not grow cynical and bitter like Izumo had, like Izumo expected her to. She stayed kind, stayed soft, kept wearing her heart on her sleeve every day rather than hiding it away somewhere no one could see or harm it, forcing Izumo to come to a realization that came slowly, then crashed on her all at once in a hospital room after rotting alive and losing her mother. Moriyama Shiemi's softness was not weakness or inexperience, neither did it come from them as Izumo had initially convinced herself. Her trusting nature, her kindness, her sweetness, and her soft, open heart were resilience; it was refusal to become hardened by the ugliness of the world- it was seeing and being the good in the world, rather than letting it twist her into a hardened, ugly person like Izumo had, and the proof of that was Izumo herself. She had done everything she could possibly have to drive Shiemi away, to distance the girl from herself, but it had been in vain; Shiemi was soft, sweet and delicate like cotton candy and she was strong and unbreakable like steel all at once, sinking deeper under Izumo's skin and burrowing further into her heart the more Izumo attempted to push her away. It was Shiemi who Izumo spilled her heart onto after losing everything, and it was Shiemi who cried not only with and for her, but out of happiness that Izumo was able to cry and laugh and feel freely now. Shiemi was not the one who broke down Izumo's walls, but rather the one who helped her break them herself, loving and supporting her and waiting for her on the other side with an open heart and open arms.
It was Moriyama Shiemi who showed Izumo that while distance was an option, it was not the only one. It was Shiemi who Izumo trusted, who she relied on, who she allowed herself to be vulnerable around despite how terrified she was- it was Shiemi, of course it was Shiemi, so how could it be anyone but Shiemi that Izumo allowed herself to give her heart to?