Not a question of grammar but one of pronunciation. I notice many educated Americans mispronounce the word "antisemitic". The word is derived from "semite" which I pronounce to rhyme with "she might" or "Sem might". I hear more often than not a transposition of the vowel sounds which results in "an-ti-sim-et-ic" (with /ɪmɛ/) rather than the correct "an-ti-sem-it-ic" (with /ɛmɪ/). (This pronunciation is listed in the Merriam-Webster entry for "anti-Semitic".)
That is, the second syllable of semitic i.e. SEM is pronounced as though it is written SIM and the third syllable IT is pronounced as though it was written ET. The word is not written SIMETIC but that is the way it is pronounced by some. A Jewish friend of mine also mispronounced the word until I asked him to pronounce it in syllable while looking at the spelling. Why do some of us, I wonder, when we add the prefix anti- mess up the pronunciation of the rest of the word?
Best Answer
I'm going to hazard a guess that the pronunciation is based on two things: widespread uncertainty as to how antisemitic is spelled, and pronunciation conditioning based on similar-sounding words.
Early confusion about how to spell the word 'antisemitic'
With regard to the first issue, I note that the spelling antisemetic is common enough in published (and presumably edited) writings since 1900 to support its own Ngram chart:
The matches underlying this chart include this one from The Advocate: America's Jewish Journal (September 2, 1922):
Earlier still is this review of Abraham Cahan, White Terror and the Red, from Book Review Digest, volume 1 (1905):
And 24 years before that, we have this instance from the Rev. Dr. Stern, "The Talmud," in Proceedings of the Literary & Philosophical Society of Liverpool (1881):
And from an undated article in The Jewish Chronicle, quoted in "Letters from Galilee," in Blackwood's Edinburgh Magazine, volume 134 (October 1883):
The spelling antisemitic is (not surprisingly) vastly more common in Google Search results, but the earliest match for that spelling is only very slightly earlier than the first instance of antisemetic cited above. From Punch, or the London Charivari (January 29, 1881), page 48:
Joseph Jacobs, writing in Trübner's American, European, & Oriental Literary Record (1883–1885) conveniently lists various contemporaneous discussion on the Jewish Question as being "Anti-Semitic," "Pro-Semitic," or "Conversionist."
Another interesting instance comes from The Catholic World (March 1889):
English words with '-etic' or '-itic/-ytic' endings
With regard to the second issue, consider the number of (more or less) common -etic words in English:
versus the number of -itic/-ytic words:
All in all, for people learning the word by hearing (not reading) it, I think it is likelier that they will assign it to the -etic class of words than to the -itic class of words, the former being considerably more frequently used and heard in English.
Conclusion
I get the impression that a sizable number of people have been pronouncing (and spelling) antisemitic as if it were actually spelled antisemetic ever since the term came into English.
In one respect, this is rather odd, given that the spelling antisemete is practically unknown to Google Books as an alternative to antisemite. But when people try to pronounce a word they are unfamiliar with, they may adapt it to a pronunciation pattern that they are already familiar with, without making much of an effort to connect it to etymologically related words (such as Semite) that they may have heard used in other contexts.
Regardless of how the pronunciation "antisemetic" first caught on, it is backed to some degree by the spelling antisemetic—which has appeared in published English for more than 130 years.