For me, it was mostly how they carried themselves.
For Origins, Morrigan was just...utterly a b. She insulted your companions, and everything and anything she disagreed with. Chantry, circle, templars, etc. Rather than having an intelligent conversation about the matter, she just makes a snide remark about how stupid/foolish something is.
I never played a male warden and never romanced Morrigan, but there is no excuse for her abandoning the Warden if they won't go through with her plot.
Atleast Solas waits until the villain is defeated before vanishing. Morrigan leaves just to spite you if you refuse her plan.
Not once does Morrigan offer an adequate explanation for her ritual; Wanting to "Save the old magics" and what not is not sufficient, when the entire world is under the belief these old magics are the cause of blights and all the world's evils. You can't just say "Well, they're wrong" and be done with it. There was no build up from her that I recall that might lead me to believe that the Old Gods WEREN'T evil, so why would she try to pass that over on me at the very very end?
It was entirely the attitude combined with the actions. Lets say Morrigan hadn't been written like a grade-a b, and instead was more of a soft-spoken apostate. Lets say she was more like Solas and was willing to offer some explanation as to why she thought the way she did, as opposed to a semi-rant that always wound up insultive and spoken in a deriding tone as if the individual you are explaining things to is a child who cant possibly understand.
I don't trust her because of how cagey she is. Honestly, I don't think she understands half of what she's doing in any of the games. She's riding off her mother's coattails, off of what Flemeth told her to do, without fully understanding WHY she's doing it, but not being willing to admit to her ignorance or listen to other people's ideas. As soon as you do something that completely throws a wrench in her plans, she throws a fit and bails. Considering her response to you disagreeing with her is to act like you're an insignificant child and deride you, that falls right in line with her attitude.
Morrigan doesn't care about Celene, she doesn't care about the Inquisition, she only cares about her goals. If there wasn't an Eluvian or ancient elven magic involved with Corypheus and his plots, I doubt she'd even help. She'd probably have bailed from the Inquisition fairly early if Corypheus was going after Dwarven something or another. If you drink from the Well instead of letting her, she throws a childish fit, as if she would have been a better fit...even if you're an elven mage with all history and magic knowledge perks unlocked.
Meanwhile, Flemeth is this thing from legend, as are all the daughters of the "Witch of the Wilds". They once warred against all of Ferelden, coming up from the South with an army. Flemeth is manipulating history in favor of her goals. How many "heroes" could there have been that she didn't assist because they didn't fall in line with her plans? Maric was helped, but why didn't Flemeth help his mother, or father, or even prevent Ferelden from falling to Orlais in the first place? You do not hear "Witch of the Wilds" and think good things. On top of that, Flemeth doesn't really deny any of these stories. There are no excuses or explainations from Flemeth, Yavana, or Morrigan. No "Those tales are exaggerated. People will always villify that which bests them, that which they don't understand. I mean no harm to Thedas, I only wish to help. If you give me a chance, I will prove it" etc. There's only "You don't understand, ignorant fool."
Out of all of them Flemeth is probably most trustworthy. I admit perhaps some things shouldn't be told, some knowledge not spread. But I still wouldn't trust her completely.
If they had put on a mask and pretended, at least, to be proper and polite, maybe I'd trust them a bit more. But all I got from any of them was just this underlying character flaw of being manipulative, arrogant, and haughty.