She knows that she's a long shot, and she'd be satisfied with Cassandra. Beforehand, she lists characteristics she sees herself as having, before saying that Cassandra only has one.
Or maybe she sees the Divine as having those qualities and just naturally strives to have those qualities herself since they are good qualities for anyone to have. Naming characteristics means nothing compared to outright encouraging the Inquisitor to support Cassandra.
Given the Chantry's prejudice against mages, if she came out and recommended herself she'd be seen as a grasping mage trying to grab power. Which she is, but she can't appear as such.
Not recommending one's self isn't the same as recommending someone else. Why didn't Vivienne tell the Inquisitor what kind of woman is needed as the next Divine and then simply ask where one would find such a woman, and speak against both Cassandra and Leliana?
Granted, Vivienne has less of a shot as Han, but for her to have any hope of being elected she has to act like she wouldn't pursue it.
You mean to manipulate the Inquisitor into supporting her? Because that's what we're discussing here, her conversation with the Inquisitor. But not wanting something isn't the same as wanting someone else to have it. Why recommend Cassandra? Why not suggest that there aren't any good candidates for Divine?
The Chantry looks down on mages trying to grab power (thanks to Tevinter) and would only consider a mage who acts like she thinks mages shouldn't have too much power and would only use her to serve the status quo if, say, someone else did give her power.
Well that's the Chantry's belief. Vivienne was raised to believe the Chant. She also demonstrated loyalty to the Chantry and supported the institution of the Circles. That was long before she even imagined the Sunburst Throne would be an option for her. So it isn't that she is trying to pretend to be anything to get on that throne, it's just that she was a natural fit. Yet despite that she recommends Cassandra instead of stating what policies the new Divine would need to put forward (which would be those Vivienne believes in). At no time does she make a case for herself or suggest anyone other than Cassandra be supported. And if the Inquisitor agrees and states he'll support Cassandra, Vivienne does NOTHING to discourage that, like "Oh well... I know I recommended Cassandra, but don't forget that she has certain responsibilities here Inquisitor. Also, just because she would be a great Divine doesn't mean there isn't someone more suited than she is." Or if the Inquisitor is in a relationship with Cassandra, "You would have to break it off with her of course, which would be such a shame Inquisitor, the two of you were meant for each other."
As Xilizhra said, Vivienne acts like she doesn't want the Sunburst Throne for herself, outwardly supports other candidates, then lists qualities for a good leader that all happen to describe herself, while "admitting" that Cassandra has one or two qualities she listed.
And in banter she tells Cassandra to work toward the qualities she lacks.
Probably covertly hoping that either the one she approves of gets it (since Cassandra is more conservative than Leliana), or hope someone (possibly the Inquisitor) recommends herself through the power of suggestion.
I think you girls are just too paranoid. I saw no power of suggestion except that Vivienne suggested Cassandra outright. Her description of a good Divine wasn't incorrect. It isn't like she meant to describe herself. She saw the Divine as those things her whole life, and naturally she aspired to have those same qualities. The Divine is someone to look up to an emulate to those who believe in the Chant.