Believe me, we didn't ask for it! It was coined by a German anti-Jewish racial agitator in the late 19th century specifically to denote hatred of Jews. (This, by the way, is why it is incorrect to say that Arabs can't be antisemitic because they're Semites, too. The word antisemitism was specifically coined to denote hatred of Jews, not hatred of Semites.)
"In 1879 German political agitator Wilhelm Marr used the phrase Judenhass (hatred of Jews) in his book "The Victory of Judaism over Germanicism Observed from a non-religious perspective." ("Der Sieg des Judenthums über das Germanenthum. Vom nicht confessionellen Standpunkt aus betrachtet.") to make hatred of the Jews seem rational and sanctioned by scientific knowledge. In his next book, 'The Way to Victory of Germanicism over Judaism', published in 1880, Marr developed his ideas further and coined the related German word Antisemitismus - antisemitism."
"The book became very popular, and in the same year he founded the "League of Antisemites" ("Antisemiten-Liga"), the first German organization committed specifically to combatting the alleged threat to Germany posed by the Jews, and advocating their forced removal from the country."
"Despite the use of the prefix "anti," the terms Semitic and anti-Semitic are not directly opposed to each other (unlike similar-seeming terms such as anti-American or anti-Hellenic). To avoid the confusion of the misnomer, many scholars on the subject (such as Emil Fackenheim and James Parkes) favor the unhyphenated antisemitism in order to emphasize that the word should be read as a single unified term, not as a meaningful root word-prefix combination."
"The term antisemitism has historically referred to prejudice against Jews alone, and this was the only use of the word for more than a century. It does not traditionally refer to prejudice against other people who speak Semitic languages (e.g. Arabs or Assyrians). "