Out of all the girls in Touya and Yuki's lives, the most important is undoubtably Sakura, if only because Yukito wouldn't even have existed in the first place if she wasn't around.
Clow Reed could see the future. He knew that in Tomoeda, a girl would be born who could become Card Mistress. He also knew that she would need help, and he set in motion events that would eventually provide that help centuries later. Since this is a site about Yuki and Touya, all that really concerns us about Clow's preparations is that he had to figure out a way for the Guardian Yue to be close to Sakura, before and after the Final Judgement, without people wondering what the hell an angel was doing hanging around a ten-year-old girl. The answer was Yukito, Yue's "false" form. As Sakura's older brother's best friend, Yukito (and therefore Yue) would be near the future Card Mistress... not to mention the fact that the magical powers latent within Yuki would be masked if he was always close to Touya, who had strong powers in his own right.
Clow also knew that Sakura's first love would be Yukito. This had a purpose too, most likely giving Yue a chance at happiness. He hoped that through Yuki, Yue would not only be able to accept Sakura as his Mistress, but that he would also love her and be able to finally get over Clow. This was actually very noble of Clow, but it was a flawed plan, because it hinged on one thing: that Yukito would eventually return Sakura's love.
Fate can wreck havoc with even the best-laid plans.
Clow's reincarnation, Eriol, said that there had been very few things he wasn't able to forsee, and that one of them was that Yukito would choose Touya, and not Sakura, as his love. And that was that.
Well, not quite of course. Yuki does love Sakura... as if she were his own sister, since her brother is the one he loves most of all. He never wanted to hurt her. And neither did Touya, he practically raised Sakura, he's what they had in mind when they came up with the concept of overprotective older brothers. He may give her a hard time, but he loves her. So perhaps the love they both felt for her was one more reason why their relationship developed so slowly.
I'm not saying that they would have given up on each other because of her. Let's be honest here, it's one thing to want to spare Sakura heartache... it's quite another to pass up on the person you love more than anyone else in the world, the person you're willing to sacrifice anything for, because your little sister has a schoolgirl crush on him. However, not wanting to hurt Sakura pobably added to their initial reluctance to acknowledge what they felt for each other.
Still, love won't be denied. When Sakura tells Yukito that she likes him, he lets her down as gently as he can. That's when she asks Yuki if it's because he already has someone he likes, and is it oniichan? Of course it is. And Yukito tells her so. And then Sakura says she's willing to let her brother have the person she thinks (the operative word here being "thinks") she loves the most as long as they're both happy. Yukito thanks her, because he does care for her and it's important to him that she accepts them and forgives them.
As for Touya... Yuki gets into a little bit of a funk over the whole thing and thinks that Sakura might not be happy to see him, yada yada yada, and Touya simply reminds him that Sakura understood and was mature about Yuki's response. Not only that, he points out that Sakura has gone back to being her usual hanyaan self.
There is a reason why Sakura is happy again, of course. This isn't a site about that, however, so all I'm saying is that the real reason why Touya doesn't like Li Shaolin is that he's "trying to take away the most important thing I've taken care of my whole life". ^.~