Also “from what I’ve read so far the Lubavitch rebbes are the Moshe Rabbeinus of the dor because that’s what they said. Did I miss something here?”
Not to my knowledge, meaning I don’t know of another source that supports that, you obviously wouldn’t find it in gemara as it wasn’t applicable then, but I think any rational person who is looking for emes will count the Lubavitcher Rebbe as a reliable source.
That’s not at all rational. We accept people as gedolim because of the opinion of other gedolim, usually from the previous generation.
In this case, some considered the Lubavicher Rebbe to be a gadol, and some most definitely did not, but outside of Lubavich, I don’t think anyone considered him to be THE gadol hador.
We don’t accept someone’s greatness on their own say so. That’s silly.
If I told you that I see Eliyahu Hanavi every night, you would probably believe me – because, after all, would someone who has gilui Eliyahu lie to you?