An official body to promote men and bring them up to equality? The problem with that, though, is that the bodies that represent women, LGBT, etc etc are trying to establish equality with men. If you accept that, for a large part of history, people who (in this country, as an example) were not white and male tended to suffer because of it, and you further accept that the situation hasn't yet reached equality (which it hasn't) then it follows that men don't even need such a body. So of course there'd be an uproar -- because, at the moment, it's largely un-necessary, so introducing it would only make sense if on a global scales the tables have turned massively in favour of non-white non-heterosexual non-men. And they haven't so it doesn't.
This is not to say that, in the face of the massive recent social changes, some men haven't quite figured out how to respond, need some support, and turn to the wrong role models. But there is, to me at least, no sign that such men need to fight for their equality against centuries of inbuilt societal oppression, in quite the same way as has been true of women.