Monster Tinder

[Amaterasu]

Ezrihel

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Vampire!

Honestly put: Ezrihel is not exactly a good fit for most monsters, especially the female types. Many of them want emotions and love in their relationships, and few have the ambitions to achieve big goals like Ezrihel.
Summing him up, Ezrihel is a big thinker: he's ambitious and likes challenges, he will set the bar high and jump it too. He's energetic and enthusiastic about what he does, as well as dominant - imposing in a way, which isn't necessarily bad. On the other hand he is a rational, logic-thinking person with little room for emotions and feelings. Which is not to say he doesn't have any, they're just deep beneath the surface. Very deep. And he will determine if a relationship is worth pursuing based on that rational, logic way of thinking. He's not going to be content with a guy or gal that brings nothing to the table.
That's why a vampire, guy or gal, is the best fit. It may not be perfect, but the best that I could come up with off the above thoughts. Vampires from a certain age on discard dead weight like emotions, things that they had as humans. They still have a trace amount of them - deep down there somewhere, but it's rarely brought out, if at all. Does that remind you of anything? Ezrihel's rational way of thinking and occasional insensitivity will thus not hurt them in most cases.
Some like challenges, others are content with building up what they have without aiming for a big goal to reach. Either one would likely join Ezrihel with his big ambitions and the determination to challenge himself, so long as he doesn't take the suicidal route. A realistic challenge, not an impossible one. I doubt that Ezrihel thinks otherwise, though.
The only thing where the cogs don't fit perfectly is energy. Ezrihel has a lot of it and he invests it. Vampires are slower, calmer, biding their time and often letting things happen rather than actively participating, as an instinct of self-preservation. They have immortality, but if they are found out they're in trouble. The exception to this are vampires who feed on human blood: they are far stronger and more ruthless than their siblings who exclusively drink animal blood, and because they have to be active to maintain that diet they don't take things nearly as slowly. On the other hand, the risk of being found out is far greater.
Either of them will pose a challenge: be it the intelligent, calm, calculating version or the ruthless, active, human blood-drinking one, they won't let Ezrihel take the lead in their relationship without a "fight". If he wants to stay on top he'll have to work to keep the spot.

Whether or not Ezrihel finds that such an involvement's long-term benefits (they're there) are worth the investment is up to him. But in the world of non-human monsters he will have to search far and wide if he hopes to find a better suited partner.