I guess the biggest question I have right now is why Judaism (and other religions) doesn't believe Jesus was the son of God? As my Mom mentioned I have started learning about different religions and studying the Bible (finished Genesis and Exodus). And I believe this is one of the main differences between Judaism and Christianity. Feel free to correct me if my understanding of it is not accurate. Appreciate your willingness to help answer some of these questions.
The term "Son of God" can mean several things, depending on the tradition you are coming from. If you believe the term to mean that we are creations of God and are all his children, then Jesus was a child of God the same as you or me. I don't think that there will be any Jews who disagree with that. In Christian tradition, the term "Son of God" is used along with other honorifics such as "Son of Man," "The Christ," or "The Messiah." It is this meaning of "Son of God" that I assume you are asking about. Why do Jews not believe in Jesus as the Messiah?
The Messiah is a very old concept that has strong roots in Judaism as well as other early religions. Though you don't hear much about it in mainstream (reform, conservative, modern orthodox) Judaism today, the concept of the Messiah was very alive in the religiosity of Jews at the time of Jesus. There were many people claiming to be the Messiah that just didn't get enough followers for their messages to survive. Today they are thought of as false messiahs. At the time, there was already a long developed tradition of scriptural interpretation that led Jews to believe certain things about who the Messiah was and the promises from scripture that he was going to fulfill. I think that, at the time of Jesus, many Jews rejected him for two big reasons. One was that he was attacking the religious organizations of the day. They thought that the Messiah should be one to save them from Roman occupation and persecution, not attack the religion from within. Though he attacked much of the negative aspects of the Judaism of his day, the people wanted their Messiah to focus on the external threat, not the internal threat. The second reason he was rejected was because he did not fulfill the believed promises of bringing about the messianic era. He didn't bring peace to the world, bring eternal life to the inhabitants, destroy evil in the world, and rule over the peaceful earth. Christianity has dealt with this problem by claiming he has done these things spiritually (washing away sins from believers, giving eternal life in heaven to those who believe, brings peace to the flock) and that he will fulfill these promises physically when he returns.
The "Son of God" title in Christianity also has some distinct trinitarian overtones in that Jesus is God the Son (Trinity being that all three--Father, Son, and Holy Spirit--are fully separate and fully the indivisible God. I can't really explain that one. It's supposed to be a contradiction. The church teaches that it is a sacred mystery.) This belief came to full fruition after Jesus had died and early Christians worked to understand who he was. There were centuries of fighting between Christians over this concept, but it is now basic, fully accepted Christianity. Another important concept that divided early Christians but is basic, fully accepted Christianity now is the concept of the humanity vs. divinity of Jesus. (The answer to this one is that Jesus is one entity, fully man and fully God. It is also taught as a sacred mystery. I can't really explain this one either.) This idea that Jesus was God does not work with Jewish teachings. In Jewish interpretations of scripture, the Messiah will be a special man, but just a man. For Jews, the idea that God would be man is unthinkable. God is God and man is man. We have a special relationship, but God would not come down as a man.
The reasons above are theological reasons for Jews to not believe in Jesus as "Son of God." I personally believe, however, that there are also a lot of cultural reasons. During the lifetime of Jesus, his followers thought of themselves as Jewish and an important debate was whether to teach his message to Jews only or everyone. They decided to teach outside to both Jews and Gentiles, but this argument lasted decades after his death. Most Jews rejected Jesus as Messiah during his lifetime, and many who thought themselves followers of Jesus rejected him after his death. It wasn't long before the early Christian church had more Gentile converts than Jewish converts. Consequently, the early church began to pull its identity away from the Jewish identity. After the Roman emperor converted to Christianity in the early fourth century, Christianity began to grow in power and for centuries after persecuted Jews for their rejection of Jesus as Messiah. Much of modern Jewish identity has been shaped by this persecution. Even though most modern Jews don't really believe in the concept of messiah from the scriptures and they don't care much about whether God would come down into a man, they do remember the centuries of persecution over this issue. Countless generations of our ancestors have been slaughtered because of their religious conviction and to convert to Christianity would feel like a rejection of their sacrifice. It is ingrained in Jews from a young age that, "You are Jewish; they are Christian. They believe in Jesus; you don't. They have killed us for a long time over this." Even when one doesn't care much about the theology, one doesn't easily forget this.
Anyway, I know this is long, but I hope it helps. Feel free to follow up with any questions you may have. I don't claim to have the authoritative answer to the question, but this is how I understand it.