*sigh* Couldn't resist after all.
Regarding the breakup scene specifically, I largely agree with the analyses that I've read so far, but one point does bother me: the cold feet. I really didn't get the vibe that Solas gets cold feet, let alone in a situation like this, it seemed to me more that it dawned on him that he literally could not tell her the truth, partly because of the incredible risk (how difficult would it have been if - going on the 50/50 chance of Lavellan's answer - she chose to respond by trying to stop him and he would have had to choose whether to kill or incapacitate the woman he loved or give up his incredibly important mission?) and partly because the entire romance from his perspective really could be perceived as a pipe dream that he indulged in, a fantasy that he could never realistically pursue because of who and what he is. For whatever reason, the romance always had an underlying illusory quality to it as I saw it, meaning that those were stolen moments with Lavellan that he could not resist, yet the dream had to come to an end eventually. So, the way I perceived the breakup was him trying to be responsible and ending it while there still was a chance to salvage both Lavellan and her feelings (no matter how counter-intuitive that might seem at a surface glance) while staying true to his real purpose, because he owes that to "the people" - the needs of the many outweigh the needs of the few or the one. Solas being a hair's breath away from revealing the truth tells me that he just saw the whole scenario play out in his head and that he resists the temptation for the first time; he might trust Lavellan to still love him despite the overwhelming truth of his identity (and he had no reason whatsoever to assume that Lavellan could accept that her boyfriend is one of her gods, particularly since thereafter he's going to have to shatter her perception of gods in general), yet even if she did accept what he says, what then? He just saunters off into the sunset with his lady love, giving up the terrible need of the people whose lives he thinks he ruined, abandoning his companions to their fate (his reaction to Grey Wardens suggests to me that, whatever his plans, he does care for them) and letting the world merrily go down its path to doom? Would it even work between them, given his lifespan and the ostensible differences between their essences? I think he realized he would be causing her more pain by letting her believe in the illusion of their romance at that juncture.
In short, I really don't think he panicked, got cold feet, lost his nerve or any other synonymous idiom, I think he realized he took his little fantasy too far and ended up hurting both Lavellan and himself by not putting a stop to it at the beginning. I think maybe even he's incredibly out of practice with regard to his own feelings - he seems to trust himself, he has exquisite control of himself in a lot of situations, yet falling in love seems like such an easy, simple thing that I think he might even have been arrogant enough to think that he could just "deal with it" and he deluded himself into thinking that it wouldn't matter, or that it could also serve him. He might even have convinced himself about that, though I think he tried to pull away from Lavellan initially because he might disdain using such a tool for manipulation, but at any rate I'm pretty convinced that he thought all of this was a harmless little infatuation that suddenly turned serious before he realized it. That was a mistake on his part as he sees it, so he has to remedy it before it gets even worse, it's better to be hated by her and to have her suffer a clean break now rather than a protracted affair that has no foreseeable conclusion on the horizon. He's not omnipotent, he cannot know what their future holds, but it's fairly easy to guess that the ending would be a bad one unless he eliminated the threat beforehand.
I can relate to that feeling, I've put an end to a relationship before because I realized that I was causing more suffering by having the other person involved wait for me for an infinity when I knew there was little to no chance of us being anywhere near each other within the next decade - and I've had it done to me, too. It's all around a nasty affair, yet I do believe clean cuts do have a purpose and there really is no way to do it without it hurting. A lot. That does not mean it's not worth the price, however, in the long-term at least, and whether or not the person doing the cutting is right in the end, it at least offers closure when that person is uncertain at best that they can actually be the partner that the other person truly deserves. (And the gods know closure is a commodity that should be cherished far more than it is.)
All in all, based on his behavior he is many things, cunning and simultaneously sensitive among them, yet I think Lavellan hits him squarely in his own hubris: he's a controller, yet he utterly fails to control this thing between them, I always got the feeling that this entire romance caught him off guard and that's how it spiraled into "real, deep feelings" having to be trampled because they grew while he wasn't paying attention.
*sigh* I so utterly failed at keeping out of this discussion.