It is conventional to give people the benefit of the doubt—to err, when possible, on the side of uncertainty and not to presume the unlikely is untrue. But it is one thing to give the benefit of the doubt in uncertain circumstances, and it is quite another to give an outsized benefit with very little doubt indeed. That, in essence, is origin of false balance.
Worse, of late the media has taken to determining what subjects are in doubt not by what evidence is available, but instead by how forcefully people argue for one side or another. A forceful but untrue statement often triggers a confused and muddled response from journalists, who, by dint of their profession, know both that the statement is painfully untrue and that to contradict it outright is painfully taboo.
Journalistic conventions, intended to ensure fair treatment regardless of personal inclination, fail abysmally when public figures refuse to play by the rules.