You are right and wrong. Islamphobia is a form of bigotry and is often related to anti-Semitism. But the meaning of the word "anti-Semitism is not defined as bigotry against speakers of Semitic language groups, just because Semite is the root word of the term. It was invented in the 19th century specifically as a term for bigotry against Jews. It was originally used by a Rabbi, then rapidly adapted by Jew haters because they believed the term "anti-Semite" sounded much more scientific than the term "Jew-hater" ....