Why does Brutus refuse to swear an oath?

Brutus refuses to swear an oath because he believes that his doing so will belittle the great enterprise that he and the other conspirators have taken upon themselves. He feels that the righteousness of their intentions is enough to keep them all honest and that if they were to swear an oath, it would suggest that their resolve is weak and would dishonor their purpose, which he believes is to protect Rome from tyranny.