Rome's flaw was giving power to Cassius who acts out of self interest.
Cassius manipulates Brutus into thinking Caesar is not worthy to be king. Cassius says "Brutus and Caesar" what should be in that "Caesar"? (Julius Caesar, 1.2.147-148). He does this because he is jealous of Caesars power.
"I was born free as Caesar. So were you" (1.2.98-99).
"You lay it in the praetor's chair, where Brutus may find it" (1.3.145-147)
To further his plan, Cassius gets Casca to lay fake letters in Brutus room supposedly from commoners that are praising Brutus saying how he should be king.
"We Shall find of him. A shrewd contriver; and, you know, his means, If he improve them, may well stretch so far, As to annoy us all; which to prevent, Let Antony and Caesar fall together" (2.1.168-174).
By Cassius suggesting that they also murder Antony, Cassius removes the veil of honor from the plan. This isn't simply about protecting Rome from tyranny; its making practical moves to protect them from further "annoyances" in whatever it is they plan after the murder.
In this scene, Brutus had just stabbed Caesar in the back due to Cassius's manipulation.
Cassius charges Brutus with having condemned one of their men for taking bribes, even though Cassius took bribes as well. He made Brutus look like a fool to cover up the fact he was too.
"You wrong me every way. You wrong me Brutus." (4.3.58-59).