Yes, Jesus who Christianity is based around lived in modern day Israel, which is located in the Middle East. All of Jesus' followers spread the message around the world. It grew mostly in the eastern European area. Eventually the Emperor Constantine forced all the Roman Empire to convert to Christianity. That is when it took off in Europe. But essentially it started in the Middle East.
Judaism certainly began in the Middle East. While there are questions as to whether Judaism began in Israel/Palestine/Judea/Canaan (all the same place), the Sinai Peninsula, or in Mesopotamia, all of these locations are in the Middle East.
As for Christianity, it depends what you define Christianity to be. If the Ministry of Jesus is considered to be the origin of Christianity, then, yes, Christianity began in Roman Palestine, which is part of the Middle East. However, if the Ecclesia (the organization of the Church) is seen as the beginning of Christianity, there were great meetings of the Ecclesia throughout the Roman Empire, but primarily in Western Anatolia, Greece, and Tunisia, none of which are typically seen as being Middle Eastern Places. The Establishment of the Roman Catholic Papacy and the Patriarchates of the Eastern Orthodox Church were primarily outside of the Middle East, in cities like Rome, Byzantium/New-Rome/Constantinople/Istanbul (all the same place), Thessaloniki/Salonika, Ephesus, Tunis, but also Alexandria and Damascus (which are in the Middle East).
The Middle East is also where Islam began.
The Eastern Mediterranean, specifically Israel.
It began in the Middle East, in the country of Israel, (which is in Western Asia.)
Christianity began in Jerusalem, the nation of Israel, in the Middle East.
The beginning of the Jewish religion can be related to either Abraham which lived most of his life in the land of Israel or to Moses how was active in the Sinai desert. Both of which are in the middle east.
Hinduism began in India, so it does not claim a spiritual home in the Middle East.
The major religions of the world began in different continents. For example, Hinduism and Buddhism originated in Asia, Judaism originated in the Middle East, Christianity originated in the Middle East/Europe, and Islam originated in the Middle East.
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There are numerous religions that started in the Middle East such as the Kemetic, Akkadian, and Babylonian faith among many other polytheistic creeds. All three monotheistic religions, Judaism, Christianity, and Islam, also started in the Middle East.
Christianity originated in the Middle East after Jesus Christ was born, and now is a widespread religion there and throughout the world. (There are other religions in the Middle East too.)
The three major God religions that were born in the Middle East are:Judaism; per Torah God revelation to MosesChristianity; per Bible God revelation to JesusIslam; per Quran God revelation to MuhammadRefer to related question below.
Judaism, Christianity, and Islam (three of the world's top 20 religions) all began there.