It was revealed that Caesar couldn't cross the river by himself and Cassius had to help save him.
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Cassius tells Brutus about the story about Caesar swimming the Tiber River because he wants to make Brutus understand that Caesar had flaws too, and he was just another simple human in the city of Rome. There was nothing special about him and people should stop looking at him as a god.
He dares him to swim in the Tiber River. He says: The troubled Tiber chafing with her shores, Caesar said to me 'Darest thou, Cassius, now Leap in with me into this angry flood, And swim to yonder point?' Upon the word, Accoutred as I was, I plunged in And bade him follow;
Cassius states that Caesar is no greater than he or Brutus (by birth), and is indeed a lesser man physically. So he feels it is wrong that he should be the one and only power in Rome, especially a Rome that was a Republic -- and therefore all Roman men share political equality (ideally). He also implies later that Caesar doesn't really like him and that upsets him: he isn't part of Caesar's inner circle.
Cassius and Caesar, according to Shakespeare's play, were childhood friends (Cassius told a story of how he even saved Caesar from drowning in the Tiber River). Obviously, they were once good friends. However, Caesar gained more power and disregarded Cassius (Cassius also became more jealous and was not so friendly in return). Caesar had new friends, like Antony and Brutus, who were loyal to him. Caesar did not need Cassius to be his friend; he felt threatened by Cassius at one point. He said to Antony that he did not trust him (he was a thinker, probably plotting something devious). Caesar had hubris and did not feel threatened, really, by anyone. Obviously, Caesar undermined Cassius and did not care for him as a friend.
Personification is when an object takes on a human action. An example from Julius Caesar would be: "The Tiber trembled beneath her banks."