No, Christianity was not born out of Judaism. In reality, Christianity is based on the rejection of Judaism. Additionally, Judaism is not something to be fulfilled, it is a way of life given to us Jews as to how we can live righteously.
That being said, most Christian denominations have historically taught that Christianity replaces Judaism.
Judaism, Christianity, and Islam (oldest to youngest). Islam, Judaism, & Christianity (largest to smallest).
Judaism,Christianity and Islam.
Christianity, Islam, and Judism all began from the ancestors of Abraham.
Judaism, Christianity and Islam.
Because they are two completely distinct religions. Christianity believes Christ was born & died on the cross. Judaism believes Christ is yet to come. Judaism believes that Jesus was just a prophet and not the Son of God.
Judaism and Christianity are from God. Judaism laid the path for Christianity until Christ (the Messiah) was born. God is all knowing, so the religions from God are better than pagan and false religions.
Christianity and Islam are both ofshoots of Judaism Budhism is an offshoot of Hinduism.
The area of the Mesopotamian valley saw the emergence of Judaism, Islam and Christianity.
Confucius because he was born before Jesus, and so Christianity had not yet split off of Judaism.
The biggest difference between Judaism and other religions is that Judaism has few if any converts. If you are not born into the religion, then you are not part of that religion. Buddhism, Christianity, Islam, Sikhism, Jainism all welcome converts.
The third oldest major contemporary religion is Christianity (before Jesus was born there was Hinduism and judaism)
The premise of your question is wrong as many would classify 'Islam' as a major religion and it is primarily found in the Middle East, North Africa and parts of Asia. If you were to ask, 'Why were many of the major denominations of Christianity born in WE,' then that would get another answer.