"Um achtchually" incoming.

The origin of the word "antisemitism" is not about languages. It is about race. It is based on 1770s Biblical racial terminology that broke up all humanity according to the three sons of Noah: Shem (-ites: Jews, Arabs, etc) , Ham (-ites: Africans), Japheth (-ites: Europeans, Persians).

A few decades later, a French fuckface called Ernest Renan creates a whole story about how Semites are inferior to Aryans/Japhthites and even writes a very influential book about how Jesus was born a Semite Jew but perfected himself to become an Aryan Christian.

So at this point, the term "semites" has a very clear racist sense to it. And in response to that Moritz Steinschneider, an Austrian Jew invents the word "antisemitism" in

the phrase "antisemitische Vorurteile" (antisemitic prejudices). Steinschneider used this phrase to characterise the French philosopher Ernest Renan's false ideas about how 'Semitic races' were inferior to 'Aryan races'". (src)

Then (with various intermediates) comes a German fuckface, Wilhelm Marr, who not only popularises the conflation of Semites with Jews but also proudly declares Antisemitism as an moral impertative to save Germany from the Jews and

in 1879 founded the League of Antisemites (Antisemiten-Liga), the first German organization committed specifically to combating the alleged threat to Germany posed by the Jews and advocating their forced removal from the country.

That's the story. The term originally was a bullshit racial category that happened to have some linguistic usefulness that we still retain.