We cannot just assume that since he applied for iOS something at Google that he's the best fit and what they were looking for.
Maybe the tools Google needs built are very CS heavy (hence the "Build us a Binary Tree" question)? Maybe during the interview his arrogant attitude was on full display? Maybe the interview team dug up past episodes of explosive arrogance like this very one we're discussing right now?
Even if they were looking for someone that matched his profile exactly, his post-interview display of non-professionalism is sure to hurt his chances of a re-interview anytime in the future (and quite possibly at many more companies than just Google).
He conveyed several things with this display, none good;
* he's incapable of handling rejection
* he feels entitled
* he feels he's better than everyone else
* he's unwilling to admit his own shortcomings
None of these are good qualities.