Reincarnation

When Jesus came to the region of Caesarea Philippi, he asked his disciples,  “Who do people say the Son of Man is?”  

They replied, “Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets.” (Matthew 16:13-20); (Mark 8:29); (Luke 9:18);

The Disciples named some of the earlier prophets. What does this mean? Rebirth was an accepted idea at the Time. It was only later the Church rejected this idea as a religious or philosophical concept (that the soul or spirit,after biological death,  begins a new life in a new body) as the doctrine of the eastern religions.