I can't exactly like him or dislike him. I just feel for the kid. He is isolated. He has been isolated for all his life - he has always seen things no one else saw, not even his big bro who promised to protect him. With all the accumulated emotional baggage - repressed anger towards his father, anger at his brother for never being there for him, fear of everything that surrounds him, and especially fear of himself - is it any wonder that he is explosive? He suppresses his feelings, but things get pushed past a point and his real emotions show. At the core, he is just as emotional as his sib.
And now he's so used to it that he doesn't know how to connect to people anymore. Or if he knows, he can't bring himself to do it.
I'm starting to think that Yukio will need to get seriously drunk in order to talk to his brother. Like, Shura finds out that Yukio has been saying mean things to his sib and it's making Rin depressed, so she takes Rin away. Rin goes back to check up on Yukio anyway, but finds him completely wasted... and blurting out whatever comes to mind. Ironically, this could actually really help in this case, since I believe their relationship will drastically improve if only Rin can figure out what Yukio is thinking.
He also grew up with a rather distorted view of demons. While Rin had to reconcile that he was a demon and that demons are not all necessarily bad despite one killing his father in front of him, Yukio never really reconciled it. He's been tortured by demons since he can remember, then killing the things since he was 7.
He must have known his brother was a demon for quite a while though. Shouldn't that have changed his views a bit? Or could he have been in denial to the point that he told himself that his brother wasn't really a demon since he hadn't awakened yet? But he was planning to protect him after 'in ten years time, Rin will see much worse things', wasn't he?
As for Rin and Yukio: there's just a lot going on there.
I do feel somewhat annoyed with Rin, because he does have a share of the blame. He's keeps occupied with his friends & school life. He ignores what's going on with his sib. He keeps acting like the younger sib when Yukio is starting to crack severely. He has to seriously step up to the plate and be the older sib to Yukio. He needs to take the first step, and not when Yukio challenges him. This would minimize significantly Yukio's anger at Rin never taking responsibility.
It's true that Rin is taking it easy, leaving all adult responsibilities to Yukio. On the other hand, Yukio actively claimed that role. Rin was fully willing to protect his little brother when they first arrived at the school, but then Yukio immediately established himself as a superior exorcist and Rin's 'prison guard' (and later even an official babysit from the Vatican), taking every opportunity to make Rin feel that Yukio is the more mature one and should be obeyed. At this point, challenging Yukio's leadership would only cause conflict, and Rin knows that. So he's putting up with his little brother ordering him around for the sake of peace, hoping that things will just get better over time, because he doesn't know what to do to make them better himself. All his attempts to approach Yukio so far have been shot down.
However, the way the situation is going, Yukio will explode and Rin will be shocked and Rin's shock will infuriate Yukio even more. At this rate, I fully expect Yukio to do something really cruel to Rin (like try to convince him that Shiro would have wanted him dead). Yukio can't beat up his sib, but he can mess with people's heads.
That's possible. It could also go the other way around though, with Rin doing something legitimately suicidal and Yukio being totally blown away. He also is oblivious to his brother's pain, to the point that Shiemi and Bon probably know Rin's situation better than he does at this point. If they would pick up on the signals and react in time to save Rin while Yukio hasn't noticed a thing, Yukio would simply collapse.