@RSO,
“but I still want to know how you can be SURE that he loved EVERY Jew.”
Because he wanted every single person born to a Jewish mother to have the same opportunity as you did to learn Torah, and to keep mitzvos.
No matter how far away he was, whether it be a Yid in sunny Florida, or a frozen soul out in Iceland, or a Yiddishe neshama lost in the Australian outback, to the lone Jew in Madagascar, or the young Israeli finding himself in South East Asia, the Rebbe saw to it that he would be afforded the opportunity to serve Hashem just like you do.
And I am a result of this dream that the Rebbe had. And because of my dedication to this goal, a Yid somewhere broke off with a goya, while another Yid puts on Tefilin each day, while a third goes to shul each Shabbos.
This is Ahavas Yisrael, loving every single Yid like your own child, and affording them the same opportunities as a Yid in Williamsburg or Boro Park has.