Teddie is a very naive, yet friendly and happy shadow. His only bad traits are being overly boisterous and perverted, IMO.
Shadows are what a person keeps hidden within them, consciously or unconsciously. What kind of person would Teddie have to be derived from that what is left over and denied is essentially a good human being? By his word, he inexplicably gained a conscious one day, but we have no indication that he was ever just a "regular shadow". He had to have come from someone, because as far as we know there are no shadows that simply existed independently of an ego. Even the Arcana Shadows in Persona 3 aren't guaranteed to have been created independent of a person. The Kirijo Group did incredibly immoral things after all....
I've got three theories about his origins.
A: Teddie is the shadow of someone who's a complete monster, that denies anything that could be considered good, and revels in his/her evil. It'd be what's left over, wouldn't it?
B: Teddie is derived from someone with a seriously fractured psyche, probably someone who's been isolated since they were very young. In my mind, maybe a teenager who's lived in an insane asylum since he was a child.
C: Teddie is derived from someone who's lived an awful, horrid life from day one. All the aspects of Teddie, such as his kindness, joyfulness, etc. are all things that that person would have an instinctual urge to do but never could do.
There is also a fourth option. The TV World is a materialization of human thought. Now, there are two ways it could go about. Option 1 is that Izanami created the TV World alongside the Midnight Channel and limited its scope to that of Inaba. The other is that she simply created a portal into the TV World that affected Inaba specifically, and decided to use the TVs as her portal medium.
Considering that the Shadows seem to be near endless in the TV World, it'd make more sense for the 'TV World' to simply be a different dimension that's always existed due to human thought. Otherwise you'd have to wonder where all the Shadows keep coming from; either you're fighting the Shadows of everybody in Inaba over and over again, or you're fighting the Shadows of the many people who live and have lived. Assuming Option 2, then who Teddie is derived from becomes a MUCH more open-ended, unimportant question that will probably never be answered.
There's no saying that a human hasn't entered the 'TV World' before the Investigation Team, which makes me think that Teddie is the result of a shadow devouring its originator, which resulted in it gaining cognitive thought, at which point Teddie was created. Simply gaining a conscious out of nowhere doesn't make much sense, but the Investigation Team's Shadows seem to go on and on about becoming complete. That'd make Teddie complete in a twisted sense, wouldn't it? It'd explain the anomaly that is Teddie.
Now, either a Shadow that devours its originator simply becomes a clean slate, or Teddie chose to forget his actions as a mindless Shadow. Who's to say there isn't a memory block on top of another memory block to hide Teddie's darkest memories, of once being somebody else and what he unintentionally did? Maybe there's a Teddie equivalent of Saki Konishi or Mayumi Yamano roaming about in the 'TV World', or possibly others from the past as well. We honestly have no idea just how large the TV World may or may not be, right?