Why do we say "Set a thief to catch a thief (also it takes a thief to catch a thief)"?

Meaning:

The best person to recognize a thief is another thief, presumably because they share the same way of thinking.

Background:

Apparently, the essence of this proverb can be found in Pleasant Notes upon Don Quixote, a 1654 commentary by E Gayton on Miguel de Cervantes' early 17th century work. It is also in Thomas Fuller's Church-History of Britain (1655), so presumably the expression was in reasonably common use at the time. Indeed, given that the Oxford Dictionary of Proverbs notes that Callimachus (writing in the second half of the 3rd century BC) said "being a thief myself I recognized the tracks of a thief", the chances are the expression has been around for a very long time. A similar proverb is an old poacher makes the best gamekeeper.

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