@reasoning logic,
The origins of Anti-Semitism really don't have all that much to do with the reputed intelligence/education of Jews. Israel is one of the highest educated countries on earth right now (as measured by secondary education rates) but this is actually largely a side-effect of some Russian immigration and as to the claims to genetic intelligence it largely references Ashkenazi Jews and a claimed "founder effect" that was part of their migration. In short, part of that theory is that the persecution resulted in the intelligence, rather than the converse. So scratch that whole idea as the origin of Anti-Semitism.
I think the main factor was the displacement of Jews that started by the Romans, whose subjugation of them made them a minority in their own land and started the Diaspora throughout the Roman empire. Without this they would have been a majority in their land, but were now migrants in the cultures of others (and as you probably know, minority immigrants are often discriminated against even in modern societies).
The next main factor was that the Diaspora had to deal with being a minority in many places where the major religion was Christianity (which became the official religion of the Roman empire shortly after the whole scattering the Jews thing they did), a religion whose narrative included the claim that the Jews convinced the Romans to kill one of their gods. This, together with their minority status made persecution of them popular, and apostasy from Christianity to Judaism was prohibited during the Dark Ages when discrimination was codified in laws that prohibited conversion to Judaism and that prohibited Christians from marrying Jews, Jews from holding certain offices etc.
As things eased up for the Jewry in Europe they began to play the role of money lender, which was forbidden as a profession for many Christians and which for much of history has been a bit of a despised profession (even now, with the banker hate you can see this continues) but this relative prosperity did not last long and with the Crusades (and the Christian fundamentalism that sought to make the "Holy Land" Christian) persecution of all non-Christians dramatically increased.
Then later in the middle ages, a Pope decreed they must wear distinctive clothing to identify them and the first of the "blood libel" (accusing Jews of consuming the blood of Christian babies) began and this segued into modern Anti-Semitism.
So in short, the scattering of them throughout the Roman empire is what made them a minority and then religious persecution from Christians made them a hated minority and the rest is history.