The biggest reason for me siding with Mages would probably be the note found in the Hunter's hut in the Hinterlands- of course there's other factors as well- anyways, the note was basically a diary entry written by the hunter where he stumbled across a group of Templars attempting to extort money from innocent refugees with violence, a bunch of Mages came and then a fight occurred and I'm fuzzy on what else happened but what stuck out to me was the fact that the Templars tried to rape one of the injured victims.
In Thedas, Templars wield authority and power over the Mages, I think years of treating Mages as less than human, with little to no rights due to a circumstance of birth, has eventually corrupted them beyond imagination. Think about it: years of being told that these people that you're charged to watch over are wild and dangerous, always be told to be vigilant and suspicious of them- eventually you'll forget that these people are human. Your authority and power over them will eventually go to your head, you'll think 'these filthy savages don't deserve kindness' and you'll start treating them like slaves, as entertainment, as handy little toys you can rape because come on, why wouldn't you use them? If they try to blab, say you never did it, your Templar buddies will side with you and if these mages become too annoying, maybe convince the Knight Commander to issue them the Right of Tranquility to shut them up- just frame them of using blood magic.
Now think about the Mages: Years locked in a tower, told you'd never be able to leave, told that you can never marry or have children and if you DO have children, your child will be taken from you as if you're a wild beast incapable of caring for your own child. Not all Circle Towers are equal by the way, and I find it hard to imagine that many circle towers are as easygoing as the Ferelden or Ostwick circle- many mages are like those in Kirkwall, abused and under the constant threat of the Right of Tranquility- it was blatantly told that the Knight Commander in Kirkwall handed out the Right of Tranquility like it was candy.
I think if I were born with magic and I suffered for it for years and years, it would eventually turn me desperate for freedom. While I don't condone the use of blood magic in Kirkwall or anywhere in Thedas for that matter, I can understand why: If you're constantly silently accused of being a blood mage, and if a revolt was occurring, and you think blood magic may be able to give you the power to obtain your freedom, since you're being accused of being a blood mage anyways why not use this ability? While in Dragon Age: Inquisition it's shown that not one side is innocent in this war, I feel that Mages are the lesser of two evils because if they were never oppressed, there would have been no war, Kirkwall's Chantry would not have exploded, etc. Yeah, Fiona was stupid for siding with Tevinter but when you can find no allies and when you're terrified of being forced back into your cage, it's understandable that you'd turn to those who are willing to help you. While I'm sure not every Templar is a power abusing scum bag, Templars are not oppressed, (of course you could argue that they are slightly oppressed due to the lyrium leash the Chantry has them on, but that's not true oppression because they had the ability to CHOOSE to be a Templar, and while it's sad that they're like chained dogs, I feel less sympathy because they still have their human rights) therefore if I were to think in a 'Masses before the few individuals' I'd say helping the Mages is a worthier goal for the Inquisition. Which is why while I regret losing Ser Barris, I would still never side with the Templars.
But then again, DAI is a game and you should always try the other questline cause they're super different from each other and both are really fun, I really enjoyed having Envy in my head in one of my Anti-Mage playthroughs ehe, so I would recommend trying both quests? 