Well, one of the biggest problems with MK is just that he doesn't really have any even matchups or bad stages. He can't be counterpicked per se (with the possible exception of Diddy on FD, but I don't think Diddy can handle MK on many other stages).
Let me make a scenario for you to illustrate the biggest problem with MK so far. Lets say I use Mario in tournaments. Mario has a nearly unwinnable matchup against MK (or so I hear), so I need to use a secondary to take care of MK. But who do I pick up? Snake? No, MKs have learned how to beat all but the best Snakes out there. G&W? No, he still doesn't do great against MK. So I pick the one and only character that can handle MK: MK himself. Then I play with MK until I'm good enough to have him as a second... but then I start to realize that I'm winning matches much more easily, I can't be counterpicked against, and I begin to rely on MK more and more whenever I feel pressured. And thats when I discover that my MK, a character I only recently picked up, is better than my Mario in every possible situation. Soon I just stop playing Mario altogether because it is so much simpler and more effective to just play MK.
But lets assume there is no MK anymore, and Snake is the second best. Mario has a pretty tough matchup against Snake, so I have to pick up a secondary to beat him. Who do I pick up? Well, I have my choice from DDD, ROB, Falco, Lucario, Pikachu, etc. There are quite a few characters I can choose from that do well, or even have an advantage against him (he even has a few hard counters, too). But each of those counterpick characters have their own inherent problems, bad matchups, and what not, so I can't really rely on them whenever I feel pressured against a character that goes even or has an advantage against them. In the end, I continue with Mario as my main and I use my second for Mario's difficult matchups but not much else.
Thats the biggest reason people are calling for MK's ban. In theory (and its actually happening currently), everyone will eventually switch to MK because they all need some sort of answer against him. I can honestly see MK getting banned in a few months if a counter or two is not found soon.