I commented this before, and it is so true that it bears repeating. It is still beyond logic to believe this myth. And an earlier comment stated that it is based on hergesh. I would second that motion. It is not based on logic or saichel. That is why all the efforts to find proofs for it are failures. One can take any written line and find ways to contort it to support a position, but that does not make the interpretation true, and it certainly does not make it saicheldig.
I noted earlier that chassidus Chabad has a history that dates back many generations of deifying their leaders. I do not say this mockingly. There is a degree to which all can learn a bit about emunas tzaddikim. But the extremes are never good. And many have commented that this extreme smacks of avodah zarah. My position is not that negative. i do believe it detracts from the true avodas Hashem.
But back to the point about hergesh. Emotion does not always have logical explanation, and is sometimes not even based on fact. In this case, the explanation might well have more to do with the fact that today’s Chabad is leaderless. There is a huge population without a leader. In an effort to fill that gap, the messages of the Rebbe being alive today can flourish, and so can the reincarnation of the Rebbe as Moshiach. And when one seeks to rationalize this, the logical arguments all postdate the conclusion because they are not the basis for it. It is a forgone conclusion, and the grasping at anything to support the idea are futile efforts to justify it.
While I may sometimes laugh at all this, I adopt a position of rachmanus, on so many people that could actually fulfill the mandate of Taryag Mitzvos, and also promoting the Rebbe’s derech of kiruv, without the obsession about the Rebbe. And once someone wants to obsess about something not real, the world of fantasy is limitless.