In the Catholic Church, the pope is considered "infallible" when he speaks ex cathedra. That is to say, he is not infallible when he speaks about things that don't have to do with religion. For example, he may say whatever he pleases about Economics, but no one will hold that Catholic economists will have sinned against God if they consider that the pope is wrong.
The important point here is that the pope is thought to be infallible only when he speaks about matters strictly related to the Church.
The Wikipedia has this:
Papal infallibility is a dogma of the Catholic Church which states that, by action of the Holy Spirit, the Pope is preserved from even the possibility of error [ 1 ] when he solemnly declares or promulgates to the universal Church a dogmatic teaching on faith as being contained in divine revelation, or at least being intimately connected to divine revelation. It is also taught that the Holy Spirit works in the body of the Church, as sensus fidelium, to ensure that dogmatic teachings proclaimed to be infallible will be received by all Catholics. This dogma, however, does not state either that the Pope cannot sin in his own personal life or that he is necessarily free of error, even when speaking in his official capacity, outside the specific contexts in which the dogma applies.
Now, I wonder if the Governing Body has ever claimed to be infallible. I know that in practice it is held to be, and that, in practice again, whatever they say is to be obeyed. But, how would one know when it is Jehovah that speaks through them, and when it is they themselves who are speaking?
By the way, if Jehovah were speaking through those men, I would assume Him to speak with ONE voice. That is to say, everyone would agree on everything and there would be no rule that winning a debate requires two thirds of the vote.
Does the Governing Body claim to be infallible? Or does it act as if it were? If so, can a witness, however fanatic, actually believe that they never make a mistake, or that they always speak for God and not for themselves?