Milo's problem is that he takes any negative reaction as an attempt to suppress free speech, because to his mind, he's not doing anything wrong so long as he's exercising his right to free speech. The irony is that he goes around calling himself the "Dangerous Faggott", but as soon as he says something dangerous and provocative enough to get a negative response, he backs away from it and claims to be the victim of deliberate misrepresentation by people who want to silence him on principle.
Thus his hypocrisy shows itself: he's allowed to exercise his right to free speech, but anyone who disagrees with him is trying to suppress that right. And by launching a pre-emptive attack on those who disagree with him, he's essentially saying "accept my right to free speech or be branded an enemy of a democratic principle", which is in itself a form of suppression. He wants his soapbox, but he doesn't want to hear a dissenting opinion.
Free speech isn't a shield to hide behind. If Milo wants to express his opinion, that's fine - so long as he accepts that people will disagree with him and are just as entitled to express that counter-opinion as he is to express his opinion in the first place. Because right now, it sounds suspiciously like "if you don't agree with me, shut up", in which case he has no right to call himself a defender of free speech.
I have no doubt that he loves free speech - just so long as he is the only one with a voice.