At the bottom of it all, I don't think his relationship is very complex, just requires some understanding of the lore. He's a bit of a weirdo and obsessive, and she's a demon that feeds on spiritual and romantic adoration.
We know that kid Boole is a weird obsessive from chapter 1 when he contemplates crippling birds so that they won't leave him. Similarly, adult Boole covers his room's walls with images of random redheads, and it seems the only reason they aren't all the saintess instead is because it would be a crime. His adoration for the saintess began when his father took kid Boole to see the saintess' parade. It did not fade even as political games hid the saintess from the public eye.
In Boole's time, the demon's best days are behind it, as the faith and adoration it needs to flourish have declined since the church of the saintess was established one hundred years ago (I make a distinction here between the saintess that people see and the demon within). Unable to demonstrate magic at all, the saintess is reduced to a figurehead hidden from the public eye, unable to rekindle faith. The nobility plans to do away with the tradition entirely. Boole's intervention, motivated by his adoration for the saintess, empowers the demon and foils those plans in chapter 5.
I believe that at this point the nature of his adoration shifts. He may not yet know that there is a demon within his icon, but I don't think it would matter if he did. To his way of thinking, the saintess powerless to resist the political games that installed him as her guard is no more. Defending His Rose with martial skill and isolating her from hostile interests used to satisfy his wish to be close to the saintess. A saintess that becomes queen and performs miracles again no longer depends on him alone, and indeed gains crowds of admirers. In short, she is beginning to leave him, just like the birds at the beginning of the story.
So, he tears off her figurative wings. Once the saintess' servant explains to him the nature of the demon, he offers to become the demon's closest servant by becoming the new host body. The demon accepts, not recognizing the trap hidden in Boole's words "I only wish to be closer to you, to be by your side, more so than anybody else." The demon has heard such words many times before and flourished because of it. But to inhabit the one speaking them is a first, and a mistake. Boole doesn't mean somebody that the demon inhabits; if he did, he would be just like the First King, and the demon would use her independent body to manipulate him into greater and greater ambitions for the name of her love. Boole means the demon itself, and he wishes for nothing that does not serve to keep her within him. No power except to trap her. No riches except to enshrine her. No comfort, no love except her presence.
She doesn't like it, but neither can she subvert him without endangering herself. All in all, an interesting way for a weirdo to seal a demon.