I think this is one of the weirdest of all the Witnesses' teachings.
1. There is destined to be one true religion.
2. The religion would be picked by the Messiah in the early 1900s.
3. The Messiah would do the picking from the afterlife in heaven.
The following problems occur:
1. The Messiah concept came from the Jewish religion.
2. The Jewish religion was not chosen to be the true religion by Jesus.
3. Therefore Jesus cannot be the Messiah, and in fact the Messiah concept must be false since it originated with a religion not chosen in 1919.
4. The Governing Body claims not to be inspired of God.
5. How does a group of men who are not inspired know who and when someone from the afterlife chooses a religion to be the right one?
So if Jesus HAD to chose an earthly organization now (or at any time), the next thing I would ask is: Why?
1. If this is a teaching of any particular religion prior to Jesus picking a religion as the right one, doesn't it make this requisite moot? It would already have to be the true religion to begin with to know about this requirement and future event.
2. If Jesus doesn't pick the religion that makes this requirement mandatory, then this isn't something Jesus would ever do in the first place. This means that if Jesus would not pick that religion thus indicating that any of the others or all of the others are the right one (but would somehow prove the first one true since it was the wrong religion that taught the correct requisite), this would mean the true religion would have made a false statement of prediction making it false to begin with.
3. So Jesus would have to pick the religious organization first and somehow mark it so people could see it was chosen by Jesus in 1919 (of whenever). So the religion would have to be the chosen one first before being the chosen one.
4. The organization could claim the gift of prophecy in this case, but this would make the point of Jesus' picking them unnecessary.
So if Jesus HAD to do this, and do it NOW, which organization would Jesus pick?
It would be the one that knew in advance that Jesus was going to pick it through an invisible process before it happened and then have proof of the invisible picking once it occurred.
The religion would somehow have to validate that Judaism was once correct and used by God to develop the Messiah concept in the first place, then present evidence that it had been rejected by God and was being replaced by this new group that was being chosen invisibly.
But if it was being chosen invisibly, having proof that it was chosen invisibly would invalidate that it was chosen invisibly. If you had visible proof of an invisible choosing, then the choosing was not invisible and therefore invalid.
So, in the end, the chosen true religion would have to provide invisible proof that it was invisibly chosen by Jesus (and that it was a true requisite that this was to happen when it did and how it did).
The answer: Jehovah's Witnesses. They're the only religion to have come up with such a stupid teaching that it must be them. They win!