Paul Grayson and a team of Cerberus infiltrated the Migrant Fleet and a lot of Quarians was killed to get Gillian back. For a tight-knit society, that was an act of war. So Tali has a healthy amount of distrust on anything by Cerberus. At Freedom's Progress, if Shepard wasn't there, the Quarians would have killed Miranda and Jacob. Even then, Miranda was all for taking Veetor back to Cerberus for more interrogation. None of this actually spell good first impression between either of them.
Miranda does seem capable as a leader but she doesn't command trust or loyalty from the rest of the crew unlike Shepard. That doesn't sound like good leadership qualities. Besides, Miri is an ardent supporter of Cerberus and she always make excuses for Cerberus and The Illusive Man. Remember her Cerberus-is-good talk about shock troopers? Look how that turns out in ME3.
In ME2, she's a pro-human supremacist and she's not apologetic about it. I wouldn't be surprised that Tali wouldn't go anywhere near the woman. I avoid toxic people too....
First things first, there are a lot of incorrect things in here, so let's nail them one at a time shall we?
First paragraph: I rather think that Jacob and Miranda would have killed the Quarians, what with their better equipment and getting the drop on the Quarians. As well, sans Shepard, it's probable that Cerberus would have sent a group of soldiers with them as an escort.
From what I can see, she does actually, among the crew. More than once you hear a comment by the Cerberus crew about how the Cerberus crew has faith in her abilities. As for everyone else, most don't really even try to give her a chance. And a lot of it is almost entirely from irrational and relatively unfounded reasons. There's really no basis to judge her actual leadership skills on this, due to such irrational distrust and dislike. So extrapolating that she's 'not a good leader' isn't a very credible position.
Also, I'm an ardent supporter of Cerberus. And I don't make excuses for Cerberus, I explain to you what they are why they do what they do. And I do think said shock-troops were a good idea. A great one in fact. I wish the alliance was doing that. We'd be holding out a lot better against the Reapers in the last game. But anyway, not to drag this into a discussion on the ethics and moral philosophy of Cerberus, but if you condemn them out of personal disgust with their actions (a rather irrational statement of ideology), I don't think there's much more to tell you except that you have the understanding of morality akin to a 10 year old, with no understanding of context or ambiguity.
Miranda is not a supremacist. Period. Being a Cerberus supporter does not equal a pro-human supremacist, nor does pro-human equal supremacist. Assumptions, assumptions.