Anonymous Gambito

Touga's backstory is bound not to be the exact same as the movie (After all, Nanami isn't even there with him), so I'll let myself speculate a bit. Their biological parents could have died, they could have abandoned them or sold them, or the siblings could have been removed from their care, and unless Nanami was brought in later to wherever Touga was, it's safe to assume that he spent at least 5 years with his original parents. He has memories of a different family, and of losing that family. Nanami doesn't even know about any of it. She doesn't realize there is a side of her brother that she never got to meet.

"Blood" is very important to Nanami. Blood is what Nanami uses to try and reassure herself that the parents who are cold and distant to her, and the brother who's grown cold and distant too, have an eternal unbreakable bond. It's very brittle though. Nanami constantly fears being replaced, discarded or harmed by her family. Most often by Touga, who ironically, happens to be her only blood relative there.

Her anxiety can be very easily explained by her experiences with how she was treated growing up in the Kiryuu household, but I do wonder if there's some subconscious parts of her that tap into these knowledge gaps too. I already felt like it was there, in the way her love for her brother is as protective as it is possessive, and how to protect him from harm, be it real or perceived, she can go feral, often shooting wildly at whoever she thinks is to blame, always hitting the wrong targets; and so maybe, I thought, it is possible that her anxieties are also tied to these repressed early childhood memories. Ones of once having a family, and then losing that world, being thrown someplace unfamiliar. Vague mostly forgotten memories fueling her fear of abandonment, working like a constant little nagging at the back of her head signaling to her how little blood ties really matter in the end.

"Blood" doesn't matter to Touga in the same way. He doesn't hold into a rose colored view of it. He knows by experience how easily those ties can be severed, how fickle they are. That's why when he found a little girl in a coffin, a little girl who spoke of there not being anything eternal, of how those you care about are bound to leave you, and questioning what's even the point of living then, he couldn't give her anything. He couldn't save her. He didn't know the answer for himself either.