Why does Brutus tell everyone to "fly not, stand still"?
The quote is from Act III, scene i, and occurs immediately after Brutus and the conspirators have finished killing Caesar. Cinna and Cassius are saying they should run through the streets, proclaiming liberty and freedom, and the senators are all beginning to panic, but Brutus advises them:
"People and senators, be not affrighted,
Fly not, stand stiff: ambition's debt is paid."
Brutus is trying to get them to calm down and act like the patriots they are (or that he has convinced himself they are), rather than run around looking guilty.
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Brutus tells all the conspirators to stand still and not to run for the same reason he tells them not to kill Antony in the attack. He is the only one of them in it for honor and for the good of Rome. By running after they've killed Caesar, it makes them look anything but honorable. Brutus does not want them to look guilty of something as base as murder.