Date and Mizuki are the best kind of found family because they're both deeply convinced that love is unrequited.
Date cares for Mizuki deeply but he can't be her father-she already has a father! Besides, he's so deeply fucked up. He's an amnesiac weirdo with a porn addiction he's barely qualified to take care of himself he can't take care of a child!! He looks out for her. He teaches her self defense. He buys her birthday gifts and chocolates that she likes and she gives her his bed. But he's tsundere about it, always keeps a layer of plausible deniability- it's not for you, it was on sale, it's just easier that way, don't think too deeply about it.
And likewise, Mizuki does care for Date! She jumps into danger with 0 hesitation to save him! She listens to him teaching her about stuff, be it fighting or what a chozuya is for or whatever! She trusts him and looks up to him! But she's a kid who has been neglected & abused by her parents and therefore live on the assumption that her very existence is repulsive and everyone will leave her eventually. So she cuts her losses. She bites. She argues. She yells. She insults him. If he's gonna leave anyways might as well be on her terms.
Date is I love you but I have no right to. Mizuki is I love you but there is no way anyone would ever love me back. And yet here they are, choosing each other over and over again. They. Fomily.