It's a combination of the verbal language and the body language/temper tantrums.
I watch a lot of Duke games on TV, and watch every OSU game on TV that I don't go to, and I see way, way more inappropriate behavior out of Coach K than I see out of Matta. It's not even close.
Matta doesn't embarrass me as an OSU fan. I'd be embarrassed by Coach K's antics if I were a Duke fan.
While I watch a lot of college basketball, I admittedly don't watch enough of those games to comment on whether those coaches act childishly as frequently as Coach K does. But even if those coaches you mention do act like Coach K, that doesn't excuse their behavior, does it? Isn't it just as ridiculous whether you can find a certain subset of coaches who also act like children on the sidelines?
But the larger point is that none of those coaches should treat officials the way Coach K does, especially not as often as Coach K does. And it particularly irks me when I hear Dick Vitale (and others, but mostly Vitale) laud Coach K for being some kind of gentleman. He may be a great guy off the court, I have no idea, but his antics on the court take him squarely out of being a gentleman (or even a decent person) in my book.