What does "kick him off his peg" mean?
Solution 1:
This is a variation of "take down a peg [or two]". From The Phrase Finder:
Meaning
To 'take (or pull, or bring) down a peg (or two)' is to lower someone's high opinion of themselves.
Origin
Various quantities and qualities have been measured by the use of pegs. It has been suggested that the pegs in question here were those used to regulate the amount of drink taken from a barrel, or those that controlled the hoisting of the colours (flags) of ships. Either of these might be correct although, like the 'yards' of 'the whole nine yards', 'pegs' could relate to many things.
It is interesting though that all the early citations of the phrase have a religious context. For example:
Pappe with An Hatchet, 1589 - "Now haue at you all my gaffers of the rayling religion, tis I that must take you a peg lower."
Joseph Mead's Letters, 1625 - "A-talking of the brave times that would be shortly... when... the Bishop of Chester, that bore himself so high, should be hoisted a peg higher to his little ease."
Samuel Butler's Hudibras, 1664 - "We still have worsted all your holy Tricks,... And took your Grandees down a peg."
If the pegs were some religious artifact, it isn't clear what they were. Lacking any real evidence, we can't be sure of the origin.
Solution 2:
The phrase in the article is worded as "in order to 'kick him off his peg'" rather than "kick him off a peg".
IMO, this is a combination the author has invented putting together "take or knock someone off their pedestal" with "take down a peg"
"knock sb off their pedestal" defined as
to show people that someone is not as perfect as they seem to be
The key word being the usage of the personal pronoun "his" which goes along with the "pedestal" idion rather than "peg".
Solution 3:
I believe this is a "mixed metaphor". They are sort of mashing up the common phrase "take him down a peg" (to humble a person a bit) with the phrase "knock him off his pedestal" (meaning roughly the same thing, but taking them down way more than a little bit, and from higher).
There's a whole page of other such mixed sayings I found here.