R’ Menachem,
IMHO, this is the point. The only Heter to hate a Yid is if he is no longer Achicha b’Mitzvos (subject to othe factors in addition). Anything else – personality conflicts, rivalries, etc. – constitutes Ahavas Chinam – for no reason. The default is Ahavas Yisrael. If Ahavah and Sinah can both be Chinam, then the implication is that the deafult state is neutrality. But this is not true. This is what I meant in my comment earlier by Ahavas Yisrael being stronger than Ahavas Chinam.
Anyway, to the best of my knowledge, the term Ahavas Chinam was coined by R’ Kook ZT”L. I did not know that it was used by the Lubavitcher Rebbe. These were great people to be sure! What I have written is based upon my Kabbalah from my Rebbeim.
It does not seem to me that we are in any great disagreement; ultimately, we are espousing the same approach.