Why is the 'anti' in 'anti-semitism'?

There's of course the simple detail that in the case of ageism and sexism, we differentiate between ages and sexes respectively.

Would you expect semitism to discriminate between semites? Anti-semitism doesn't distinguish people based on what kind of semite they are, but on the fact that they are. Anti-sexism would in the same way not distinguish between sexes, but discriminate people because they have a sex.

(Strictly speaking, anti-semitism does distinguish between semites, because Palestines are semites too, whereas the term usually is specifically about Jews.)

The terms "ageism" and "sexism" demonstrate a use of the -ism suffix similar to "racism". When it's not describing prejudices or prejudgement, the "-ism" suffix seems generally to be used to refer to a doctrine or process, as in "capitalism", "baptism", etc. Applying the suffix to "anti-semite" would seem to be consistent with the latter use, whereas "Semitism" would seem to be the former.

The suffix itself does not imply judgement or value of its subject. "Ageism" may refer to discrimination against the young even though that may not be what usually happens, just as sexism may refer to discrimination against men even though that is less frequent. If the subject implicitly applies prejudice, that's up to the subject (as with "anti-semite").

It seemed to me that these two terms might exist because of "racism", which I thought was another 20th-century invention (the word, not the act), also denoting a prejudice. Indeed, a Google ngram search seemed to support the timeline.

But on closer inspection, the term "antisemitism" appears to go back to the 1880s, and "racism" goes back quite a bit further:

It still appears that "ageism" and "sexism" were inventions of the 1960s, but as you've no doubt already discovered, the word "antisemitism" dates back to 1879 and was invented as a more scientific-sounding replacement for "Judenhass". So it seems that "Semite" and "antisemitism" are unrelated terms. Legacy often trumps logic in language.

I propose that your difficulty with this word is not because of the prefix "anti" but because of the suffix "ism".

There are hundreds and hundreds of words in English that end with "ism". (3824 according to the free dictionary.) Here's a few of them: minimalism, classicism, capitalism, literalism, polytheism, etc., etc.

If you view the Wikipedia page on the suffix -ism, you'll find that words with this suffix are often used to describe philosophies, theories, religions, and social movements. So while one person may have a semitic view of things, another may have an antisemitic view, hence semitism and antisemitism. This is how the suffix is used in the vast majority of cases.

The words ageism, sexism, and racism (and perhaps a few others) are really the exceptions to the rule here. For example, racism is not a philosophy or a theology at all. Rather it is used to describe a process of discrimination. It was in the 1920's when the word "racism" really took hold and in the 1960's and 70's other words to describe discrimination were invented that borrowed the morphology.

It makes sense to precede any of the words minimalism, classicism, capitalism, literalism, polytheism, etc. with anti, but not the words that describe discrimination.

So, antisemitism then, is a word of discrimination, not because it ends in ism, but because by definition an antisemite is one who is against the beliefs of Jews. Notice also, that we don't say the person is an antisemitist as we would refer to a person practicing racism as a racist.

To be clear, it is the word antisemite (no ism suffix) that makes us understand discrimination in this sense, not semitism or antisemitism.

While I will certainly not claim that English is logical, I think there's a subtle distinction between the two types of words. In such -isms as sexism, ageism, & racism, the discrimination is on the basis of the thing, not the thing itself. That is, sex, age, and race are things that exist*. No one is against them, just discrimination on that basis.

With anti- words, the opposition is to the thing itself. People are opposed to Jews, capitalists, Nazis, or whatever, because of their nature.

*And let's not get into discussions about whether they're actually social constructs &c.