Odd, because the manga is implying that an open heart, and honesty is what makes you a good exorcist. I assume Liu, like Yukio, is vulnerable to demons because of the emotions and experiences he supresses and has never gotten over. Anti-demon beliefs can only get you so far.
Having an open and honest heart is ideal! It ensures that the character is strong and insusceptible to manipulation. Rin has what it takes to be a great exorcist.
On the other hand, Liu's gripe with Rin is their clash in perspective. The way I see it, exorcists, first and foremost, exorcise demons. Saving people is a byproduct. Rin, however, wants to do it the other way around and play devil's advocate (ooh, pun). Picture a doctor deciding against treating a disease, because he doesn't wish harm to the bacterial organism. Liu, as well as Yukio, find that way of thinking extremely problematic. Essentially, Rin is too sweet.
For that matter, the difference between Liu and Yukio is the timing of their experiences. Liu has venerability on his side. He spent many long years rationalizing his choice, regardless of lingering feelings, to toughen it out. Yukio doesn't have that luxury, because his problems revolve around Rin.
And Rin is, well, around.
That said, they've both got issues! Liu is probably more lenient with Rin than Yukio is, because he doesn't have the same stressors and can actually relate, to a point, which makes him far better off than poor Yukio. He's a little more open-minded and malleable, but also a lot more confident in his beliefs.
I'm not sure of what I'm saying anymore.
