@oratio is correct. But the scene is not really about the question or the answer. I believe it’s meant more as a way to illustrate Igby’s rebellion and failure to conform to his family’s expectations. The question is not profoundly intelligent, it’s Igby’s way of challenging authority, it’s not an insight to the meaning of life or religion, but to show us the headmaster’s lack of patience with Igby (by not even bothering to answer the question). The headmaster could have answered the question, but choose not to.. it has nothing to do with him being stunned or dumbfounded. He simply chooses to ignore Igby for now.
The scene continues with Igby’s mother entering the room while being welcomed by the headmaster as he congratulates her on her other son: Oliver, Igby’s older brother and the perfect son (also the one who did succeed according to the headmaster). We end the scene with the headmaster saying: ’But of course we are here to talk about Igby….’. After which the scene transitions to Igby being dragged out of the room into the hallway by his mother, where we find out Igby was expelled, and his mother blames everyone but herself before sending him off to military school (she has lost all patience with Igby as well).
Some quotes from the hallway scene where we first learn about Igby’s position in the family:
Igby’s brother Oliver: ‘Igby is not my fault’
Igby’s mother: ‘Did you even think for a second how this reflects upon me?’
Anyway, if you ask me, you missed out on walking away early :) I just watched it again a few days ago, and it’s one of my favorite movies.