R' Shneur Zalman of Liadi says in Chapter 32 of Tanya (colloquially called the "Lev" of Tanya - the heart of Tanya) that one can have true love of a fellow Jew only if he views his soul primary and his body secondary (since our souls have one root, so there is no cause for division, machlokes, etc.) Therefore,
The Alter Rebbe’s answer follows from his previously stated principle that the essence of ahavat Yisrael lies in giving priority to one’s soul rather than to his body. This indeed is the basis of the entire Torah — as the Alter Rebbe continues:
This is what Hillel the Elder meant when he said in regard to the fulfillment of this commandment, "This is the whole Torah, whilst the rest is but commentary," and so on. For the basis and root of the entire Torah are to raise and exalt the soul high above the body, reaching unto the Source and Root of all the worlds, and also to bring down the blessed light of the En Sof upon the community of Israel, as will be explained later, i.e. into the fountain-head of the souls of all Israel, to become "One into One." This is impossible if there is, G-d forbid, disunity among the souls, for the Holy One, blessed be He, does not dwell in an imperfect place, as we pray: "Bless us, O our Father, all of us together, with the light of Thy countenance," as has been explained at great length elsewhere.