In Act I, Scene 3 of Shakespeare's As You Like It, what reason does Duke Frederick give for his decision to banish Rosalind?refer to act 1 scene 3

In Act I, Scene 3 of Shakespeare's As You Like
It, Duke Frederick orders his niece, Rosalind, to leave his court. He wrongly
accuses her of treason. When his own daughter, Celia, protests the banishment of
Rosalind, Frederick responds as
follows:

• Frederick
  She is too subtle for thee; and her smoothness,
  Her very
  silence and her patience,
  Speak to the people, and they pity her.
  
  Thou art a fool. She robs thee of thy name;
  And thou wilt show
  more bright and seem more virtuous 485
  When she is gone. Then open not thy
  lips.
  Firm and irrevocable is my doom
  Which I have pass'd upon
  her; she is banish'd.

This is a
revealing speech for a number of reasons, including the
following:

• Frederick is the
  character who might most reasonably be described as “subtle,” especially if that word
  suggests a person who is devious and not to be
  trusted.


• Ironically, in the very act of attacking
  Rosalind, he calls attention to some of her virtues, including her
  “patience.”


• The fact that the populace feels “pity” for
  Rosalind suggests that many people in the dukedom possess a virtue that Frederick
  himself seems to lack, thus making him seem uncommon in his
  hard-heartedness.


• The true “fool” in this play is
  Frederick himself, in the sense that he behaves unreasonably and
  unwisely.


• By making this kind of decision and speech,
  Frederick will in the long run be robbing himself of his own “name” or
  reputation.


• Frederick assumes that his daughter shares
  his own selfish motivations.


• Frederick believes that
  Rosalind is a traitor or potential traitor, but he has already proven himself the true
  traitor in the play by usurping his brother’s dukedom.
  


• Frederick speaks with an unbending determination that
  implies his enormous pride – a central sin for Renaissance
  Christians.