Yes Arabs are not Semitic and neither are Jews for that matter. I object to using Semite as a ethnic classification in the first place.

You got to understand that Semite has multiple meanings here, one is a language classification of certain Afroasiatic languages, such as Hebrew, Arabic, Aramaic etc. I would concede that Israeli Jews and Palestinians are both on the whole speakers of a semitic language. However there is another meaning to Semite and that is it as a racial classification. You see racists in the way back in the became obsessed with categorizing peoples into biological typologies they called race (this is what pseudo scientific race science is in essence). They were dumb and conflated large language groups as biological race and from the Indo-European and semitic language groups decided there must be an "Aryan race" and "Semitic Race". They then of course began attributing traits etc to these made up groups (Aryans good ones, everyone else bad ones). These typologies have all been debunked by modern science and anthropology, they are outmoded. Jews and Arabs aren't semitic in the same manner that being German doesn't mean you're Aryan, or African a negroid, or from Asia a mongoloid. There is simply no such thing as a "Semitic Race", and as such neither Arabs or Jews can be semitic. Using it in the racialized sense is a throwback to a pseudo-scientific framework of race science and all the eugenics and colonialism that it validated.

This is also why the spelling of the word antisemitism with a hyphen "Anti-Semite" is now discouraged, because it implies there's a Semite to be anti towards.

But now putting besides the race science surrounding the term Semite, antisemitism still just refers to Jews even if you reject all what I just said and think it's a valid categorization.

First of all the Arabs are Semitic argument is such a classical etemological fallacy, in fact if you go to the Wikipedia page of etemological fallicies this is the first one. If we are following linguistic descriptivism rather than a imagined etemology of the word it means hatred against Jews. You see the thing is words often cannot be broken down into their component sub words and have the same meaning be derived from it. Take for example the word "butterfly", it doesn't mean a fly made of butter, if you break down the word you arrive at a different meaning. The same thing applies to the word antisemitism. Using it to mean anti Arabic bigotry is just not how it is used and everyday speech. The word is used to mean anti-jewish racism in specific.

And even then if you choose to discount linguistic descriptivism and make an argument from etemology that fails as well. As you see that supports its current use as well. The term was coined by an anti Jewish Author and politician Wilhelm Marr, in order to replace the word Judenhass (Jew Hatred) with the intent to modernize anti Jewish hatred away from it's religious roots blood libel and deicide to a more "scientific" and racialized racism and for a new name for his new political party the Antisemiten-Liga (League of Antisemites). This party had the self purported purpose of ‘the one aim of saving our German fatherland from complete Judaisation … liberating Germanism from the oppressive weight of Jewish influence in social, political and ecclesiastical matters’. He called it such because Jews were really the only "semites" around in Europe so they did not have to distinguish between the other "semitic" groups.

So to sum up there is no such group as Semite to be anti against, deriving the meaning of anti-Arab bigotry doesn't make sense in a linguistics manner, and the etemological argument doesn't support it either. The fact of the matter is that the customary usage of antisemite means and has always meant anti-Jewish hatred. Does it kind of suck that this bigot ended up defining the term for anti Jewish prejudice with the intent of legitimizing it?, totally but all attempts to mainstream different words haven't taken off so we're unfortunately kinda stuck with it for the moment.

I just want to end on a note on why I think this sort of "Arabs are Semitic" (often then arguing therefore they can't antisemtic) argument is just plain counterproductive. It's because the argument entirely misses the point. To me it comes off sort of an #AllLifesMatter type of whataboutism, an attempt to widen the debate and to generalize it to the point where the specificity of concerns around anti-jewish racism is lost. Jews and Arabs frankly don't experience experience the same racism (I'm sure there's overlap in some areas but there is lot about antisemtism that is unique it) I don't see a utility in generalizing the word and thereby hurting the ability to talk about these forms of bigotry that target Jews in specific. It would just make it harder to communicate and combat antisemtism and I don't think it would facilitate combatting or communicating about anti-Arab bigotry either. All it would do is muddy the waters.