".... No less surprising is Moses’ insistence: “Do not despise an Edomite, because he is your brother.” Edom was, of course, the other name of Esau. There was a time when Esau hated Jacob and vowed to kill him. Besides which, before the twins were born, Rebecca received an oracle telling her, “Two nations are in your womb, and two peoples from within you will be separated; one people will be stronger than the other, and the elder will serve the younger.” (Gen. 25:23) Whatever these words mean, they seem to imply that there will be eternal conflict between the two brothers and their descendants.
At a much later age, during the Second Temple period, the Prophet Malachi said: “’Was not Esau Jacob’s brother?’ declares the Lord. ‘Yet I have loved Jacob, but Esau I have hated…” (Malachi 1:2-3). Centuries later still, Rabbi Shimon bar Yochai said, “It is a halachah that Esau hates Jacob.” Why then does Moses tell us not to despise Esau’s descendants?
The answer is simple. Esau may hate Jacob, but it does not follow that Jacob should hate Esau."
Rabbi Jonathan Sacks
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It would seem odd that the Navi says in the name of Hashem that He hates Esav and yet we are told by Rabbi Sacks not to hate Esav.... "Maybe" Esav is evil and good hates evil. We hate Nazis. We hate Arab terrorists. We hate all those people who carried out Pogroms, inquisitions and who imprisoned Jews under the most horrific of conditions over the centuries.
But wait - what about the pasuk לא תתעב אדומי כי אחיך הוא?? Note that it doesn't say to love Edom. It says not to be "מתעב" him. The Rambam in the Sefer Hamitzvos paskens this pasuk as one of the 613 mitzvos!!!
והוא אמרו יתעלה לא תתעב אדומי דור שלישי וגו''.