Docetism

Because some people didn't like the Incarnation

Out of all the ideas within Christianity, the incarnation is the one which causes the most discontent with people outside of Christianity. The incarnation, the Christian idea that part of God, the Son, came to earth in a physical body as Jesus, is unacceptable to many people. This idea was the seed of one of the first major controversies which Christians had to deal with; it is even discussed in the New Testament.

Some people in the first 100 years of Christianity accepted parts of the faith (such as loving everyone) and altered other parts (such as the incarnation). This is how it worked. As Christianity was developing, another unrelated belief system also developed known as Gnosticism.

Levels of gods. The highest god—referred to here as GOD—was only concerned with spiritual matters.
Far below, a lesser god—referred to here as god—was not drawn to spiritual matters and, instead, created everything physical, including the earth. (Note: although this god created everything physical, it was still a spirit.)
Therefore, if people want to understand spiritual matters, they have to reject the lower god and pray to the highest GOD. By doing this, GOD gave them a higher, secret, spiritial knowledge. These people were called Gnostics.

Some people liked parts of Christianity, such as Jesus' teaching on love, but not the incarnation. They decided to combine Gnosticism and Christianity and create a “better” understanding of Jesus; this belief is known as Docetism. Instead of God becoming human, these Gnostic Christians believed that

GOD sent a messenger to earth,
who was Jesus,
and then, since Jesus came from the highest GOD, who focused on spiritual matters, Jesus was pure spirit and not physical. The word often used to describe this state is “phantom”: he appeared to be physical but was not.

The Docetics, also called Gnostic Christians, believed that Jesus was a messenger from GOD, who taught about Truth, and who was not physical: this rejected the Incarnation.

Gnostic Christians reinterpreted Gospel stories to defend their beliefs:

According to the Gospels, Jesus walked on water. This was proof to Gnostic Christians (Docetics) that Jesus wasn't physical, since physical people don't walk on water.
According to the Gospels, Jesus was arrested and forced to march to the place where he was crucified. But along the way he fell: the Romans forced Simon of Cyrene out of the crowd to carry the cross the rest of the way, then Jesus was crucified. But Gnostic Christians altered the story and believed that Simon of Cyrene was crucified not Jesus: Jesus had disappeared since a "phantom" cannot be crucified.

Note: The words “gnosticism” and “docetism” do not appear in the New Testament. These teachings were not given that name for hundreds of years, yet Docetism specifically is described in the New Testament. For example:

Paul may have been thinking about Docetism when he wrote Colossians 2:9 around AD 61: "For in Christ all the fullness of the Deity lives in bodily form."
John was definitely writing against Docetism in these two letters from the late AD 90s:

I John 4:2b: "Every spirit that acknowledges that Jesus Christ has come in the flesh is from God."
II John 7a: “Many deceivers, who do not acknowledge Jesus Christ as coming in the flesh, have gone out into the world.”

One of the best descriptions of Jesus being physical is a story involving an Apostle. That Apostle is Thomas, and within Christianity he is known as "Doubting Thomas"; this story is found in John 20:24-31. After Jesus was crucified and rose from the dead, he appeared to most of the Apostles: Thomas was absent. They later told Thomas that they had seen Jesus, and Thomas replied that he would not believe unless he touched the wounds in Jesus’ body. Later Jesus appeared to Thomas and said “Put your finger here; see my hands. Reach out your hand and put it into my side.”

Three things are significant about this story.

This story is only in the Gospel of John, which was the last Gospel written. (Around AD 90)
Out of all the stories that John could have told about Jesus after he rose from the dead, why pick this one? Think about it this way: who really cares if Thomas had trouble believing or not? John added it most likely because by this point (in the late first century) Gnosticism was a greater danger than when the other Gospels were written.
Yet John knew what he was doing. Gnostic Christians were spreading stories and teachings about Jesus to “prove” that he wasn’t physical. So John included a story in his Gospel that directly opposed the Gnostic Christians and that early Christians could use to prove the incarnation. After all, what better proof would you need to show that Jesus was physical than a story where Jesus actually says “Touch me”?