The initial question: Why have Jews been hated through the centuries?
Several reasons:
Until the recreation of the State of Israel they have always been a minority wherever they've lived. Therefore easy prey to blame for any problem which arises. Since they are spread around more than any other people (as percentage of population) more opportunity exists for hatred.
Through the centuries they never had a home country to back them up - hence vulnerable to every whim that human nature can dream up for attack.
The hatred for Israel now is a residual of those centuries as well as a component of Islam's attack on the West. The hatred for Israel that exists in the West comes from the leftwing which hates success of any kind.
When Jews are given an opportunity to exercise freedom, they are substantially more successful as a group well beyond what their numbers would indicate. It's not easy being the holders of the largest number of Nobel Prizes, demographically speaking. Success engenders jealousy.
Instead of celebrating their success - it's damned. Much like Justice Clarence Thomas or Dr. Rice are damned rather than celebrated by the leftwing as well as the Black "leaders."
Over the centuries, time after time, Jews were invited in to various countries to help market forces uplift the general economic statis of the host country. Then when this had been achieved it was time to expel them and confiscate their property - than to pay one's debts. With no home country to come to their aid they were easy prey.
Jews are persistent. Persistent in their beliefs, persistent in their quest for quality of life and mind. That engenders jealousy.
What did that hate include besides jealousy?
They were blamed for things like the Black Death - when they too were dying in the thousands. They were blamed for the death of Jesus, when in fact for Christianity to be the religion it is - Jesus had to die - otherwise there is no resurrection. No matter who killed him...the fact is "no death - no resurrection." Christians probably would readily agree that both Jesus' life, death, and resurrection are G-d's plan....why blame anyone for carrying out that plan - be they Romans or Jews or Martians? But ignorance doesn't reason this out and strikes out in blind hatred.
Anyone who is a minority....
or worse than that a distinct minority
and even worse a successful minority..
is a prime target for hatred.
But is the initial premise true? Are Jews universally hated? Not really. Jews lived for over 3000 years in India. Tolerant India had no problem with Jews - never hated them, never killed them, and found them to be good neighbors.
China was home to Jews for over a thousand yeas. China was a tolerant host and likewise had no problem...never harmed their Jewish citizens, and lived well with them.
Is it an accident that both India and China have ancient cultures...sure and confident in their own identities and therefore not threatened by a successful minority? In fact both India and China appreciated the unique and ancient culture that Jews represented.
So maybe the answer to the question "Why are the Jews hated?" Should be: Why were the countries who killed them in their millions so hateful?
Very interesting point.