First of all... Indiana doesn't really count as "the north". Usually, the North refers to New England and some of the surrounding states. Having lived in New England, and in FL (and having had many interactions with "real southerners" from surrounding states.... we all know that most of FL doesn't count as the south either.) It has nothing to do with people from the south being "too polite" or "too patient". I think that's more of a New York thing than a northern thing. Even then, only certain parts of New York (maybe some parts of Jersey too).
Really, the making fun of lies around the concept of the stereotypical "redneck". When northerners make fun of southerners, they're really making fun of that stereotype - the person who sits on his porch with a shotgun and chewing tobacco, waving the confederate flag, unable to speak English (I'm not talking about the accent, I'm talking about the words.."y'all aint got none'a that there thingy do ya?"), hating the lazy nig**rs and those damn Mexicans. This is the stereotype that gets made fun of. Having now lives "in the south" (near the south), I've seen people who fit this stereotype exactly... though it definitely makes up the minority of the south (from what I"ve seen), than the majority. I've never seen a northerner make fun of the typical "southern hospitality type" of southerner. It's always the negative stereotype of the wife-beating, black-hating, confederate flag-toting southerner.
As far as why southerners make fun of northerners, I don't see this quite as often. I HAVE seen it, but I don't think I hang out in the right circles to experience it enough.