The original question had to be edited. On first glance, Bruno's mispronunciation of Auschwitz can be seen as representative of how much of a child Bruno is. Certainly, Gretel points to this. Bruno's inability to pronounce the word "Auschwitz" correctly is what she uses as reflective of his infantile ways. Boyne's use of Bruno in this manner reflects his youth, as opposed to Gretel who has put aside her dolls in favor of becoming enamored with Nazi propaganda.
Yet, I think that Boyne might be striving for a more symbolic purpose in Bruno's mispronouncing of the term. "Out- With" is a misread of Auschwitz, which is a misread of what human beings do to one another. Bruno cannot pronounce the name of something that should never be uttered. The death and dismay that is associated with Auschwitz is what Boyne is suggesting is wrong with the world. Bruno cannot "get right" that which is "wrong" in general. Boyne uses Bruno's inability to pronounce the name of the camp as reflective of how Bruno might be right in a world that is wrong. Everyone who sees Auschwitz as acceptable and "correct" might be in the wrong and Bruno might be the only one right for he cannot correctly articulate that which is wrong in the first place. I think that the symbolism of Bruno's mispronouncing of the term lies here. Bruno's sense of honor and dignity is something that cannot comprehend and articulate the reality behind a place like Auschwitz. In this, Boyne might be suggesting a condition of seeing the world as what should be from what is. Through this, Boyne is clearly articulating a condition of repudiation of what reality once was in terms of the Holocaust.