No, the term "antisemitism" was not coined by Israelis. It was adopted by Jew-haters in Germany because it sounded more "scientific" than the older term Judenhass (Jewhate). Recall, many people once believed that the idea of "race" was a scientific explanation for differences among peoples. They believed that anthropology, linguistics, and evolutionary biology would back up their local cultural prejudices.

However, the German antisemites never cared about Arabs, Ethiopians, or other Semitic-speaking peoples. It was always about Jews: they wanted support for the political position that Europe's Jews were a foreign corrupting influence who should be expelled or killed. "Antisemitismus" was a thin façade of bad social science over a continuation of the same Jewhate that Martin Luther and medieval passion-plays had expressed.

https://en.wikipedia.org/wiki/Antisemitism