In a fascinating Purim Sicha from תשכ”ה, the Rebbe summarizes the entire issue of why an antisemite hates a Jew and what is a solution if he intends to do bad things to us.
The following is a summary of that Sicha:
There are two main reasons for antisemitism.
1) Our very existence disturbs them. 2) Our existence makes them feel an inner emptiness. There is no cure for the first kind. The only way to feel good is to eradicate the Jews from the face of the earth, R"L. With the second kind, there are two possibilities. They begin to live a life of meaning and purpose or try to exterminate the Jews R"L to fill their inner void.
The Rebbe then goes on to explain what our only solution for this predicament is:
We as Yidden, cannot rely on our non-Jewish neighbors. אנו אין לנו להשען אלא על אבינו שבשמים: when we place our trust with the Aibishter, and follow the directives of the מרדכי of our דור, in how to behave with our בכל אשר תעשה, then we can be sure that ונהפוך הוא and it will be ליהודים היתה אורה ושמחה וששון ויקר.
פורים תשכ"ה שיחה ד' (סעיפים כ-כט) | PDF | אודיו
The Rebbe's 7 Rules for Combating Antisemitism