take (someone) down a peg, to

take someone down a peg (or two)

 and take someone down a notch (or two); knock someone down a peg (or two); knock someone down a notch (or two)
Fig. to reprimand someone who is acting too arrogant. The teacher's scolding took Bob down a notch or two. He was so rude that someone was bound to knock him down a peg or two.
See also: down, peg, take
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

take (someone) down a peg

To reduce the pride of; humble.
See also: down, peg, take
American Heritage® Dictionary of the English Language, Fifth Edition.

take (someone) down a peg, to

To deflate or humble someone. This term alludes to lowering a ship’s colors, which were maneuvered by means of pegs. The higher the colors were flown, the greater the honor. The term was already being transferred by 1664, when Samuel Butler wrote (Hudibras), “Trepanned your party with intrigue, And took your grandees down a peg.” John Ray’s Proverbs (1678) defined it as “to remind upstarts of their former condition.” It is still widely used.
See also: down, take
The Dictionary of Clichés by Christine Ammer
See also:
  • brought
  • champ down on (someone or something)
  • bog
  • bog down
  • bogged down
  • blaze down
  • blaze down on (someone or something)
  • chomp down on (someone or something)
  • come a gutser
  • beat down on (someone or something)