Exactly. The private organization hosting the Labor Day parade invited the Pride group to join in. The mayor used his political power to force the Pride group out, which is indeed a human rights issue. Unfortunately for the mayor, it's also a civil rights issue and and a First Amendment issue. He tried to skirt the problems raised by a government actor suppressing public speech by citing unspecified safety concerns, but that's highly unlikely to pass legal muster, especially since he's going to have to provide evidence of the danger he alluded to, which he has neglected to do so far, leading people to believe that the evidence doesn't exist.
He was pretty flat-footed about the whole thing, admitting in his email to the pride group his real motivation — his desire for personal, ideological reasons that Pride not have a presence in the parade.