It is very weird that in the phrase "anti-Semitic" most people understand Semitic to refer to Israelis, while today most of the Semites are Arabs.
The term "Semitic" is not at all appropriate as a linguistic term, but nobody has succeeded to find any acceptable replacement.
In the Bible, the populations were divided in 3 groups, sons of Japheth (hence the American word "Caucasian", because Japheth is a term for Caucasus), sons of Shem and sons of Ham. From Shem and Ham, the linguistic terms "Semitic" and "Hamitic" have been derived.
However the use of these words for classifying languages has been based on a misunderstanding of the Bible. In that classification of the populations from the Bible, the division did not have anything to do with their descendance from ancestors speaking a common language, but it was completely determined by the political dependence of the territories by the time when the Genesis was composed.
The so-called sons of Ham where those who lived in territories dominated by Egypt ("Ham" is related to the native name of Egypt; Egypt is a Greek word), while the so-called sons of Shem were those who lived in territories dominated by Babylon or Assyria ("Shem" may be related to "Sumer").
As one of the examples that demonstrate that the Genesis classification was political, not linguistic, the Phoenicians were sons of Ham, not sons of Shem, like the Arabs and Hebrews, despite the fact that the Phoenician language was a Semitic language almost identical to Hebrew (the main difference between Phoenicians and Hebrews was in religion). The Phoenicians were sons of Ham, because at that time most Phoenician cities accepted the suzerainty of Egypt, even if they had a certain autonomy.