Simple. It is because he plays for the Bears, doesn't particularly like the press and doesn't go out of his way to smooth the egos of sportswriters. He doesn't do anything any other competitor does, especially one that is supposed to be a leader on the team. He gets angry, he tells people off and hasn't always had the best things to say after football games. I have never heard him throw a single teammate under the bus but somehow he got that rep.
Heroes and villians sell press copy. If everyone was a 'good guy' in the press's mind then there wouldn't be any drama. It is almost WWE like the way the press treats these players. Cutler is called a bully and a whiner and a crybaby and everyone eats it up. This is the same group that took a convicted dog fighter and turned his return to the NFL into some kind of heroic comeback. It builds up guys like Flacco and Shaub as 'elite' then asks all of the 'what is wrong with this guy?' questions when they fall short. Their goal is to create heroes and villians. TO, Suh and Cutler were villians. Brady and Manning are heroes. Reality doesn't matter.
You would be amazed at the number of people that actually believe the crap that the press posts about him. One buddy out here had no idea the stuff he does for Juvenile Diabetis research. Another is amazed that he is the team captain, and one of the more popular guys in the clubhouse. Not a single one of them has ever heard Jay Cutler actually speak. I still get crap about how Cutler sat out the second half of the NFC Championship game even though he was taken out by the coaches. Reality doesn't matter, they still question his toughness even after all that has happend over the past few years. Cutler will deal with that for the rest of his life.
Is it fair? No. Is it realistic? No. But that is what the sporting press does. The whole dirty business is in place to sell copy and that is what it does.