"Arabs cannot be anti-Semitic because they are Semites."
Yes, Arabs are Semites. No, anti-Semitism doesn't mean being against Semites. It is more complicated than that.
The word 'anti-Semitism' was coined by proto-Nazis in the late 19th century to refer specifically to Jews. Luckily for Semites, the Nazis didn't hate most of them; they mostly hated Jewish Semites. This meaning will not ever change. It's use by Nazis became viral, and at this stage, so did the act of anti-Semitism as Jew hatred become viral: it was called the Holocaust.