The only real answer I can give you about why violent anti-Semitism has existed for the last 2500 (give or take a few centuries) years is because they occupy a place outside of the norm.
In the years before Christ and before the Diaspora really expanded beyond the Near East, they were an isolated pocket of monotheists who clearly followed their own distinct culture and religion within polytheistic societies. An important aspect of this was that, in these societies, the citizenry were often expected to worship the king/emperor as a god. The fact that the Jews would not do so rather complicated things. In addition, the province of Judah/Judea was a highly sought after seaport, and the presence of Jews in that area—not to mention their occasional armed assertion that they should have sovereignty over it—really pissed off whichever ruler was in charge of it during said armed assertions.
Then Jesus and the War of the Jews (or Christianity and the War of the Jews if you prefer) happened. In the centuries leading up to the conversion of the Roman Empire to Christianity, Jews continued to hold an uncertain place. This is where the whole “the Jews killed Jesus” thing comes into play.
The Romans killed Jesus—he probably pissed off the Jewish authorities, but those authorities lacked the ability to carry out criminal procedures. The Romans killed Jesus because they were freaked out by how influential he was becoming, and crucified him. Crucifixion was a fairly commonplace mode of execution for anyone from pretty criminals to revolutionaries within the Roman punitive system. However, because the early Christians were heavily persecuted in the Roman Empire, they certainly couldn’t indict the Romans for the killing of Jesus, so they ascribed it to the Jews.
Because of “The Jews killed Jesus,” and the concept that Jews represented nothing more than God’s reminder of the incompleteness of life before the arrival of life, Jews became oppressed and marginalized in Europe in a far different way than they had been under the Romans and the ancient governments.
Medieval Jews were frequently expelled from various European polities. Lynchings were frequent; especially on Easter. Massacres also occurred in retribution for accusations of blood libel—the ritual killings of Christian children at the hands of Jews.
Because money-lending was considered to be an unclean, un-Christian occupation, it was one of the few avenues open to Jews which allowed them to make a living. Certain other business related occupations were open to them as well. Although these were the occupations Jews were forced into by their oppressors, it quickly became another excuse used by Christian society to incite violence and hatred against them.
Things were better for Jews in the Islamic World. There were laws which made it clear that Jews were second-class citizens, but they had freedom to work and operate in public and worship and attain an education without living in fear of being massacred by their surrounding neighbors. In fact, some of the most celebrated works of medieval Jewish scholarship were produced by this Sephardic community.
As European society moved out of the Middle Ages and into the Enlightenment, attitudes towards the Jews began to change. It is not that mainstream society had ceased to discriminate against them, but that the Enlightenment had altered their thought processes. They still vehemently disliked the Jews, however, Enlightenment thinkers believed that, as humans, Jews deserved official Emancipation. The understanding was that, once Emancipated, Jews would no longer have a reason to remain Jewish and would convert to Christianity.
Around the nineteenth century, European governments began to extend some rights—or at least official toleration—to the Jewish community. However, Jews remained hated and mistrusted because, as far as Christian society was concerned, Jews would be the other for as long as they refused to convert to Christianity. They believed that Jews viewed themselves not as Germans or French or Viennese, but as Jews first and everything else second; the notion that Jews had primary loyalty to each other over international boundaries was deeply disturbing to these populations. They also mistrusted the ability of Jews to be able to truly assimilate because of certain aspects of public modes of Jewish worship, such as the prayer to return to Eretz Tzion.
There also remained hatred towards the Jews in rural populations because rural communities resented the economic stranglehold they perceived the Jews as having over them.
In the modern era, it was primarily the idea of Jewish separateness, and Jews as the controllers of money which fueled anti-Semitism. We can see these forms of anti-Semitism coming out in the Dreyfus Affair, and in the writing of the Protocols of the Elders of Zion.
However, European Jewry DID modernize, or assimilate. Certain populations assimilated so completely that they would have been hard pressed to acknowledge their own Jewishness. That is why the policies of the Third Reich came as such as shock to German and Austrian Jews: many of them had simply ceased to think of themselves as Jews. The problem was that non-Jewish society never stopped viewing them as such.
And that brings us to the Holocaust. I am not going to discuss anything past the Holocaust because I feel that that material is too political to fall within the scope of this blog.
So, in conclusion, Jews are hated and have been hate for such a long time because they are the Other. They never fit into any society’s concept of “the norm” and always insisted upon living outside of it, refusing to give up their traditions, laws, and ways of life. Their Otherness frustrated, angered, and fostered resentment in those surrounding them, creating situations in which they were forced into certain paths and modes of behavior because all others were closed to them. Later, these paths and behaviors became additional avenues for violence and hatred.
I hope this has answered your question. This post, of course, highly simplifies a crapton of information because I am trying to give you an overview of ~2500 years of history. This post is also centric on European Jews in the Common Era simply because I haven’t devoted much study to the experiences of Jews outside of this sphere (I do however, have to read a book about Jews in the Ottoman Empire for a class next week and I am super-excited to learn more about that community).
Because this is such a broad overview, please feel free to ask me to discuss a narrowed down version of this. Like, instead of “Why does anti-Semitism exist?” I can also answer more specific things like “What fueled nineteenth century German anti-Semitism,” or “What was Roman policy towards the Jews?” etc.
If you would like me to make this rebloggable, let me know.
ETA: I posted a rebloggable version