According to Rabbi Michael J. Cook, Professor of Intertestamental and Early Christian Literature at the Hebrew Union College, there are ten themes in the New Testament that are the greatest sources of anxiety for Jews:
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The Jews are culpable for crucifying Jesus - as such they are guilty of deicide
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The tribulations of the Jewish people throughout history constitute God's punishment of them for killing Jesus
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Jesus originally came to preach only to the Jews, but when they rejected him, he abandoned them for gentiles instead
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The Children of Israel were God's original chosen people by virtue of an ancient covenant, but by rejecting Jesus they forfeited their chosenness - and now, by virtue of a New Covenant (or "testament"), Christians have replaced the Jews as God's chosen people, the Church having become the "People of God."
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The Jewish Bible (the so-called "Old Testament") repeatedly portrays the opaqueness and stubbornness of the Jewish people and their disloyalty to God.
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The Jewish Bible contains many predictions of the coming of Jesus as the Messiah (or "Christ"), yet the Jews are blind to the meaning of their own Bible.
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By the time of Jesus' ministry, Judaism had ceased to be a living faith.
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Judaism's essence is a restrictive and burdensome legalism.
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Christianity emphasizes excessive love, while Judaism maintains a balance of justice, God of wrath and love of peace.
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Judaism's oppressiveness reflects the disposition of Jesus' opponents called "Pharisees" (predecessors of the "rabbis"), who in their teachings and behavior were hypocrites (see Woes of the Pharisees).
Rabbi Cook believes that both contemporary Jews and contemporary Christians need to reexamine the history of early Christianity, and the transformation of Christianity from a Jewish sect consisting of followers of a Jewish Jesus into a different religion.
Source: https://en.wikipedia.org/wiki/Antisemitism_and_the_New_Testament