Putting it bluntly, Yukio's an asshole. He rejects compassion from others and the idea that he can feel empathy for others. He's deeply screwed up, and even his twin brother can't reach him. Yukio would only be abusive to anyone who tries to help. Just look at how he shoved off Bon and mocked Rin. He can't fathom anyone could care about him, let alone love. If he encounters it, he'd push back hard. Honestly I think he'll even do this to Shiemi just to drag himself through the dirt because Yukio hates himself more than he cares about Rin or Shiemi. Until he pulls himself out of his extended tantrum, he would be a terrible romantic partner.
I also really dislike "I can fix him" narratives. I love Yukio, but he's got a vicious streak a mile long.
I really wouldn't label anyone with deep seated self-deprecation and hatred as an "asshole" though. They're a victim more than anything, if they have, to date, failed to find a single person who is able to understand the fact that their mindset is messed up enough to think of themselves as absolutely unlovable, and then reach out to them accordingly, in a mature way*. Everyone in the series is fifteen though, so you can't really expect that out of them. And Yukio, who in so many ways is the same fifteen year old, has been shouldering more than his fair share for *far too long*. If anyone's an asshole, it's Shiro, for his misparenting, and then Mephisto just adding onto it after his death.
*EDIT: Shura's the only person who gets close to doing this
Also to add on a bit more,
now Yukio
has cracked. It's just that he has been cracking for a while, and it's a pity that none of the people close to him could really do anything about it, and it just goes to show how little they understand him. Having good intentions and being compassionate in your own way to help someone just sounds good in a textbook. I'm not saying it's wrong, but it seldom really works in the real world with people whose psyches already are too messed up to see these types of things very clearly. Also even as he was totally losing it, Yukio *did* reach out to Rin with regards to how he was bothered about their origins, and Rin in that moment was a total idiot (not wrong, because he was honest, but an idiot nonetheless - it's totally empty for Rin to *ask* Yukio to confide in him, and then basically give him a response which just alienates him further once he does... in a fragile situation like that, you don't need honesty as much as you need words which will provision comfort and understanding).
With that said, lol, I guess I totally misinterpreted the purpose of the thread or something. It was pure unadulterated crack that he should find a romantic partner in the Illuminati. As I said already, I don't think it should actually happen, nor do I believe it will.