This subject has been discussed previously, and it has been shown that the holy spirit was reinstated once Rutherford passed off the scene and the Knorr/Franz era began. So, Rutherford's claim that the holy spirit had been taken away is "old light," like so many other teachings. I would like to be able to read Rutherford's comments in context once all his books are on line.
That being said, the ministries of the Holy Spirit and the angels are not exclusive of each other in the NT. See Heb 1:14; 6:4; Acts 2:1-4; 5:19-20; 15:28, etc. What makes Rutherford's statements so controversial is the removal of the Holy Spirit and the exclusive use of angels.
Rutherford may have had in mind the passages in John which refer to the Spirit as the Paraclete ("Comforter" - KJV; "helper" - NWT). Jesus is portrayed as referring to his own imminent departure, and saying to the disciples: "Nevertheless I tell you the truth; it is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. . . . Howbeit when he, the Spirit of truth, is come, he will guide you into all truth . . ." (16:7, 13) The Spirit operates in this capacity during Jesus' absence. While the Gospel of John does not have much to say about the Parousia (second coming), the inference could be drawn that with the return of Jesus the Spirit would be withdrawn in the capacity of Paraclete. Jesus would once again be with his disciples in person to comfort and teach them. For Rutherford, this coming of Jesus apparently was not his Parousia-coming in 1914, but his coming to the temple in 1918, for then the spiritual resurrection (supposedly) also began in fulfillment of the promise: "I will come again, and receive you unto myself; that where I am, there ye may be also." (John 14:3) If this were his understanding, Rutherford could claim that he did not mean by the removal of the Spirit a complete absence of the Holy Spirit from the earth, but rather that the need for the Spirit as a guide or teacher was no longer there. However, a fallacy here would have been the belief that angels were being used instead of the Spirit - for even angels would have been agencies substituting for an absent Jesus, whereas the inference we have drawn is that once Jesus had returned there would be no need for anyone or anything else to take his place. So then, if we follow JW thinking to its logical conclusion, we have a situation similar to the Memorial which is still observed, namely, that the "coming" of Jesus in this sense is not accomplished until all the anointed have finished their course and passed off the earthly scene - for he comes specifically for them to take them home to himself.
There is, however, a larger context in which to view this. It is the question of how far removed a new religion (whether a sect or a cult) can distance itself from the parent religion without losing its identity. For example, Christianity found it necessary to retain the Old Testament rather than being entirely independent of Judaism. Both Russell and Rutherford found it necessary to state that dispensational changes were taking place which necessitated their distancing themselves from Christendom. Russell claimed that certain "truths" specially meant for the harvest period were now due, and Rutherford needed to distance his presidency even further from Russell - so that the corresponding distance from normative Christianity was increased. By the time of Rutherford's death there were questions as to whether the new religion could even be considered Christian anymore. Whether conscious of this fact or not, Knorr and Franz had to discard some of Rutherford's more extreme positions, including the removal of the holy spirit. And this is what they did.
But, as I say, I would like to see of there is any explanation given in Rutherford's own writings.