It was mentioned in the episode by one of the characters, Cameron i think.
House was obsessing over it because if Kutner was murdered then he hadn't missed anything, hadn't NOT seen that Kutner was actually feeling this way. (You all know how House hates to miss things)
If Kutner had been murdered then the guilt placed on House and the team for not noticing Kutner's state of mind would have been lifted.
House is obsessing because,.... If it was a suicide ,then House thinks he should have seen the clues and seen it coming and should have been able to prevent it. ..... House would rather it have been a murder because he himself would not feel responsible and could have no way of knowing that it could happen ,...AND HE HAS FOUND OUT THE GUY WHO MURDERED KUTNERS REAL PARENTS ( and who Kutner testified against because he saw it all ) WAS DUE FOR PAROLE IN THE VERY NEAR FUTURE , but at the end House found out that this guy had died two months ago anyway , so he had to accept very reluctantly that it was indeed a suicide , and thats why he went to Kutners house instead of the funeral ...to try to make some sense of it in his own mind xx
it seems House was trying to find a rational explanation to his death, since he didn't give any signs that he would kill himself. it's House's way of dealing with what happened, because, as KJ said "he didn't see it coming. It gets under his skin. He is the man who can't rest until the puzzle is solved. (...) he worked in such close proximity to Kutner and didn’t see it coming.