So there's this wonderful bit of interaction that Hawke had with Merrill, right after Anders destroyed the Kirkwall Chantry, that pretty much summed up for me why he opted to support the Templars right then. He explains, that it isn't any real desire to annul the Circle, not even willingness to act one way or another. In a better time and place, he would've happily and merrily continued trying to convince Meredith and Orsino to work together, rather than bicker and fight each other at every turn. But Anders didn't allow that to happen, he forced them all towards action. And so Hawke had to choose the very best that he could, even though he dang well didn't want to.
See, Hawke is a mage. Which seems to make the choice pretty straightforward. Except I like defying simple characterizations and I figured that Garrett Hawke hasn't had an upbringing or any kind of experience enough, that he'd be so simple by the time all's said and done.
If you play through Legacy, Malcolm Hawke is overheard wishing none of his children were born to magic. It made me think that even a mage-born Hawke wouldn't have been raised to see magic as any particular gift. But rather a challenge and a burden, something that made life all that much more difficult. It left my Hawke with a sense of undue obligation and responsibility, a rather difficult load to carry at every turn, and way too many people constantly counting on him. By the time he's grown, he has no real appreciation for magic or his own ability to use it, and would probably be perfectly content to enter the Circle if it weren't for his mother and then those of his companions who truly need him.
So when Anders spouts all his rhetoric about freedom and how every mage should be on his own to do as he will, Hawke is totally opposed. He's more inclined to think of the Circle as a place of safety and security for mages, far from all those who'd harm them simply for being different, and free of the burden of constantly worrying what might happen if they lose control. He argues with Anders constantly on the question. Then, too, Carver joins the Templars, and no matter how much Anders argues, Hawke can't believe that every Templar is some evil-doing nutjob like Alrik. Not when his own brother wears that shield.
In the end, Hawke chooses to bring immediate control and order to a situation that's completely blown apart. Going into the Gallows alongside the Templars is the only way he can see to bring the entire thing to a quick close, to end it before the entire city is embroiled in the most horrendous violence possible, where the people themselves attack the Gallows directly. And he utterly refuses to make any choice that has him fighting his own brother, too. It helps that along the way he manages to save some few mages, to boot. For him, it's not the choice he wanted, it's the choice he thought best between two equally ugly options.
I rather think he's entirely sick of all of it by the time it's done, too. Hawke's story seemed entirely sad, if you ask me. I kinda figure that he eventually leaves Kirkwall out of pure sadness. Like the only bright thing in his life ends up being an elf who chooses to love him back for some strange reason he can't entirely wrap his head around, hehe. And maybe he leaves in order to keep from dragging himself and his loved ones through anymore crap, too.