It's not funny, it's inevitable - Arab and Israeli tribes were all Semites (which is why accusing Arabs of being anti-Semitic is annoying, as it implies that we are not Semites) they share a common genetic and cultural heritage, and their languages evolved from common roots. If you ignore the current crazies on both sides, Judeo-Islamic tradition makes far more sense that Judeo-Christian one does.
All you said is right, but please don't mix concepts.
It's funny because Classical Arabic do not sounds like Hebrew at all (except some very basic words).
But Ancient North Arabic very similar to Hebrew and other Canaanite languages.
Languages and genetics are two very different things.
The reason, that Ancient Hebrews spoke Semitic language doesn't mean they were "Semites". Many people in Canaan were speaking Semitic languages, so it might be Ancient Hebrews just adopted local lingua-franca.
We didn't invent the term 'anti-Semitic' - I believe it was coined by a rather anti-Semitic German. We're all very aware Arabs are also Semites, but the word as it's actually used is solely about Jews, and everybody knows this.
If you can get everyone to switch to something like 'Judaeophobia', I'd personally have no objections - but sometimes you've got to work with the vocabulary that already exists.
