I thought it was done to point out the similarity in their personalities and behavior. Kyle is actually a lot like Sigmund; it's not as noticeable because he treats Sigmund very differently from the other characters. This troper assumed it was sort of an Inferiority Superiority Complex he had involving Sigmund, where Kyle uses mockery on the ones he considers lower than him - Fanboy and Chum Chum. Sigmund does exactly the same thing to Kyle, but we don't know whether he's just a Jerkass or it's also part of that same complex. (Of course, Kyle and Fanboy and Chum Chum react to this treatment differently, so it doesn't come off as so obvious). — Nashimi
In the episode when Lenny time travels to destroy the Frosty Machine so he can never see Fanboy and Chum Chum, the kids put on a 5-second Just for Fun funeral. How the heck to kids know about death at the age of five?
In his debut episode, Kyle casually references the time where he turned his teacher into food and ate them, meaning Kyle has no problems with actually killing people.