Can you help me to understand why the Jewish faith does not believe that Jesus is the Son of God?
There are several reasons most Jews do not accept that Jesus is the Son of God. Some have nothing to do with scripture. Others are based on what Christians would generally call a misunderstanding of scripture.
Probably the biggest reason some don’t believe is the way Jews have been treated by people who called themselves Christians. Although there were only Jewish Christians for approximately ten years after Jesus died, non-Jewish (Gentile) Christians have become the majority. After a couple of centuries Gentile Christians started blaming the death of Jesus on the Jews. For centuries non-Jews who wanted something the Jews had used this as an excuse to persecute them and take their property. As late as Shakespear’s day (1600’s), Jews were being forced to convert (at least in name) or be exiled from their home countries. In some countries this lasted even later than the 1600’s. Some Jews came to America, for instance, to avoid conversion or persecution. These forced conversions and burnings at the stake, or other punishments, have given the word “Christian” a bad name among Jews. In this they are understandably correct in opposing Christianity. Unfortunately some greedy or misguided people have brought shame on the name of Jesus the Messiah, and they will have to answer to God for that.
A second important reason is that many Christians have insisted on the doctrine of the Trinity. The Jews see this as belief in three Gods rather than one. The absolute central idea of Judaism, written on their doorposts and recited several times a day is, “Hear, O Israel, the Lord your God, the Lord is one: and thou shalt love the Lord thy God with all thine heart, and with all thy soul, and with all thy might.” (Deuteronomy 6:4-5) Therefore, anyone who worships “the Father, and the Son, and the Holy Spirit” must be worshiping three gods. We can explain this away in all sorts of ways. We can say they are three aspects of one God, or three personalities in one “godhead.” One way to deal with this objection, though, would be to do away with the traditional doctrine of the Trinity, which takes considerable twisting of scriptures to try to prove. That doesn’t mean that Jesus is not the son of God. The writings of John (the gospel of John, 1 John, 2 John, 3 John, and Revelation) are all to show that Jesus is truly God’s son. Just as my son shares my name and attributes, so a son of God would share his “godness.”
A related objection is that God is spirit, and could not have been “made flesh and dwelt among us.” (John 1:14) Again, this is what John calls the spirit of antichrist. (1 John 4:3) We can’t explain how the son of God could become flesh, but John says that he did. Again, this objection depends on whether Jesus is considered equal to God or just nearly so.
A big difference between Judaism and Christianity is an understanding of the role of the Messiah. Christians say that Jesus was Messiah in accordance with prophecy, and that his work and kingdom was spiritual. “My kingdom is not of this world.” (John 18:36) Jews, both at the time of Jesus and now, believe that the Messiah will come to set up a physical kingdom on this earth. The land promise given to Abraham is of great importance. Of course, many Christians will argue that they broke that covenant and gave up the promises of living on the land forever. After all, the second Temple was destroyed and Israel as a nation of God has not existed for almost 2000 years.
I must point out that some Jews accept that Jesus is Messiah and the son of God. Some of them worship with non-Jewish Christians. Others call themselves Messianic Jews and try to keep their Jewishness as well as believing in Jesus. Some are convinced by the writings of John. More are convinced by the arguments in the book of Matthew or Hebrews. Many may be converted by showing them the timeline of the “seventy weeks” in the book of Daniel. Some face rejection or persecution from their own families or their Jewish acquaintances for their beliefs.
See What Does the Bible Say About..Jewishness? for a response to this answer.