The ruling faction can label their rivals in any way they deem necessary. The moral labels that trigger emotions directly and completely bypass the brain's logical circuits are preferable. "Evil," "immoral," "terrorists" - all perfect labels to make sure people will automatically take the ruling faction's side without stopping to think about it, and without considering any information.
The Council does it. It's their privilege as the ruling faction. The asari found the Citadel first. That's the only real difference between the asari dominance and human aspiration - the asari were first, and humans were late. They're in power, and we're not. Yet. Hence, they employ heavy artillery against us. Like labels, yes.
And Cerberus is the only active pro-human organization in space that's not completely subdued to the Council. That worries the asari. We threaten their power.
Why does everybody think that Spectres, the Council's lawless enforcers, are heroes, and not terrorists? Because the Council, the ruling faction, declared them as such. They give a lofty speech, create a solemn atmosphere around the title, viola.
Why does everybody think that Cerberus are evil, even though they're a really small organization that operates in secret, and little is known about them, and their body count is completely insignificant in comparison, say, to blue suns? The Council propaganda. Who cares about the blue suns? They're just bandits without a purpose beyond personal profit. Cerberus has the purpose. And the Council doesn't like it. They won't surrender their power. They like it, you see.
As for the turians and salarians, they became too powerful, and the asari realized that since they can't defeat them, they need to join them. So the empire of one became the empire of three. They balance each other, since warring with each other would result in too heavy losses to everyone. The Council is here to uphold "the galactic stability," all right. If by galactic stability you mean the asari-turians-salarians empire status quo.
The "lesser species" tolerate this situation. Several reasons:
1. The Council is too powerful to challenge directly.
2. After the Council uses the other species to benefit their own, they try not to destroy their tools if they can afford it. No reason to go to war with them to the death for your species' survival. Just be content existing at the brink of extinction, if that's what your pride allows you.
3. The Council dangles the possibility of joining them like a carrot in front of the "lesser species", should they ever become powerful enough. As long as this possibility still exists, they need not actually give anyone a seat on the Council. And the volus are starting to realize that.
4. You don't even have to deal with the Council at all unless you have ambition for power. So there's no need for conflict if you're content with living in degradation and stagnation, and don't have any ambition to fulfill your genetic destiny by reaching for advancement. In fact, your species can continue living in the dirt of their own homeworld, never reaching for the stars, and disappear just as unnoticed as they arrived, without leaving any lasting impression on the galaxy.
If that's what you want.
Of course, the situation in the galaxy won't favour the species who don't actively reach for advancement, because they will just be wiped away by the Reapers if they're too lazy to develop in time. Evolution is a hard mistress.
So, the Council pretends to act in the interests of all the species. And they benefit everyone, indirectly, as any balance of power would benefit anyone who doesn't want to change it. But that's still asari dominance. And they're incompetent.
The only thing they're good at is mind control - people skills. But they're useless when it comes to survival and progress. They're too slow. Too complacent. They live for too long. They have no pressing need to do anything. Not active enough. Not curious enough. Not aggressive enough. They're unable to respond to the situation in time.
They failed the ultimate evolutionary test. They completely missed the Reaper threat. Despite all the warnings, all the signs of danger. Despite being outright told what was going on. Several times.
If you're unable to face the unpleasant truth, then you're not fit to rule the galaxy. Leave this job to someone who can face that truth and do something to change it. Someone like TIM.
Sure there's no direct "proof," but how can they take that risk, the defenders of the galaxy? Trillions of lives are at stake! They can't take the risk, they must act on suspicions. The only proof good enough would be the Reaper army itself. Anything else could be written off as geth advanced tech.
Let's just face it. The Council is unable to do their job. They weren't the ones who saved the galaxy twice. It was humanity. And now we're going to do it for the third, and the last time.
And we better be given the power and the tools to do this job right.
The Council must step down and let someone who's more capable of upholding galactic stability do the job. Otherwise, the galaxy will fall prey to the next external threat, because it wasn't ruled by the species who's good at dealing with that sort of thing.
Yes, yes. There's an essential difference between the Council and Cerberus. Here it is: the Council failed to save the galaxy. If things were left to them, the Reapers would've already taken over. And Cerberus brought Shepard back and were the only ones doing something about the Reaper threat. Here's your essential difference.
Look past the labels. Look at the core of things. The galaxy is still alive because of Cerberus. And no thanks to the Council. That's the core of everything.