Speaking from the view of someone who completed the game and watched the original anime. Teddy is basically a walking anomaly as he's a
Shadow who became human after interacting more with people
Because of this his ego manifested reversely. In Persona 3 the concept of a controllable ego was something that only a select few people had.
However in Persona 4 all who enter the tv world must confront their ego and accept it in order to manifest a persona. Most people are killed by their ego instead.
Teddy, as he interacted more with the protagonist and the investigation team slowly began to ask himself things he never did before:
- Who am I?
- What am I?
- Why am I here?
- Where did I come from?
He slowly but surely realized the simple fact of what he was but refused to accept it. Because of that inner conflict he discovered his own alter ego which manifested and after accepting it he learned to wield the power of persona.
Most people fight to discover their inner-self he fought because he already knew his inner self and wanted to be different.
Because of that he along with Naoto and kanji has one of the 3 most interesting inner-conflict that is portrayed marvelously in his character development in spite of him being a "joke" character.
In respect to your last comment about Izanami, because of Teddie's origination it makes sense to infer that he had a closer connection to Izanami than the other character's shadows so the wordplay by both dialogues adds credibility to that hypothesis.