I don't think this has ever been clear.. The two explanations I've heard are..
a) After taking the throne in heaven in 1914 Jesus inspected the religions claiming to follow him, because (only)the Bible Students were preaching his word, no part of the world (peaceful and neutral), loving, encouraging, and feeding one another spiritually, he placed his appoval on them as his "faithful and discreet slave"
b) The other, more complicated, explanation (which I heard a lot as a young Witness in the 1980s) was that again Jesus" came to the spiritual temple" and "judgement was to start with the house of God" and he was to "serve as a refiner to cleanse the sons of Levi". He found the Bible students sincere but in need of cleansing as they still were practicing pagan customs and had compromised their neutrality during the World War - cited was the fact that some of them had gone into the armed forces and a Watchtower had recommended participation in a National Day of Prayer suggested by the (US) President. As a result he let them be disciplined by going into " captivity to Babylon the Great"
Allegedly, at the instigation of their religious opposers, Watchtower representatives were charged and jailed on grounds of sedition based on inflammatory anti-government remarks in the publication 'The Finished Mystery'. Later they were exonerated, cleared of all charges and released.
This was seen as a sign that they had been sufficiently disciplined .and they 'cleaned up their act' cutting all ties to, false religion, the political system, and paganism. Now re-vitalized by Jehovah's approval they set out to Advertise the Kingdom , and recieved Jesus' appointment as his FDS
At least this is what I recall...It's all been overturned however since "The Governing Body has decided' that they, and they alone are the faithful discreet slave.