What really has the libs, and the dummies, upset is that the MSM no longer has exclusive control. That is it in a nutshell. Trump is using twitter to get his message out and it is resonating. Libs and dummies hate that.
Yep, that's it and they hate it. The message now doesn't have to be filtered through the NYT, and they can't stand it. I remember one DUmmie just seething: "HE WILL NOT STOP TWEETING."
That was on top of a list of imagined crimes. Like, "he will not stop killing millions of people. He will NOT STOP TWEETING!" 
It's actually a tad more than that. They hate that Trump is bypassing, or just outright trolling, the MSM, and the country is listening to him, but they also were convinced that Obama would be the "internet President," and it just hasn't worked out. Nobody gives a damn about his online video addresses that he put out there to replace the weekly radio address. Obama routinely tweets flattering pictures of himself on important dates (seriously, go look at that feed and see how many times he inserts himself into some picture depicting an event), but otherwise gets no messaging out via internet at all. His biggest "success" at being the "internet President" was doing an "interview" with some loon sitting in a bathtub full of fruit loops (how incredibly fitting!). Trump, OTOH, grabbed the internet by the ***** and showed 'em all how it's done.
Yet another Obama failure, and they can't stand it. They won't ever admit it, but it's plainly obvious that when they are bitching about Trump tweeting, it's because he is successful at it and Obama failed miserably.