Not to mention, it changes from campus to campus. For instance, I believe Pi Kappa Alphas are normally known as Pikes, but for some reason on my campus they're known as PIKA (almost always all caps too). Similarly, I've usually heard Lambda Chi Alpha shortened to Lambda Chi, whereas we called them just the Lambdas. Both of these would sound weird on a different campus, but anything else would sound weird on my campus. Last year a bunch of freshmen on campus started a movement to shorten Sigma Chi (always known by the full name) to Sig Chi. It may even catch on.
To sum up, it just is. It doesn't really make any sense if you sit and think about it. Why did Phi Kappa Sigma get "Phi Kapp" and not Phi Kappa Psi? And the KKG/KAT question in interesting. I would guess the "A Chi O" vs "Alpha Chi" question has something to do with the presence of Chi O on the campus, and also what they're trying to rhyme it with for songs
That's all.