Dave, the terms semite and semitic were coined in the late 18th century. August Ludwig Schlozer, who coined the terms, had the idea that languages like Hebrew, Aramaic and Arabic all originate from one original language, a 'proto-semitic' one. Extending that thought, if they all spoke one language, they must all be one people, a semitic people. Moritz Steinschneider was the first to coin the term antisemitic. If you know of any earlier mention, please share. He used it to describe the French scholar Renan who held that the European races were superior to Semitic ones. Renan himself used the term semitic reluctantly, for want of a better one. Many German writers and demagogues in the 19th century used Semite to reffer to Jews. Steinschneider aside, the person who came up with the noun and concept that is antisemitism was Wilhelm Marr. Marr also coined the term Judenhass (Jew-hatred).
He founded the Antisemite League in 1879.He wanted to stop what he saw as the Jewish threat to Germans. You wont find mention of Arabs or anyone but Jews in Marr's rhetoric.

If you want to use the Biblical classifications, the Phoenicians aren't the children of Shem!