Shakespeare has used the word fawn rather than a synonym such as a flatter to describe his actions because fawn is more negative, suggesting manipulation of another for personal gain.
The word fawn implies a young deer that represent immaturity. It means it could be used to express the pessimistic manipulative behavior of a person.
However, flatter is giving a positive perspective that arises from a praising scenario.
Thus, it fawn word is more appropriate to show how Cassius is influencing Brutus for his personal gain.
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