Why is St Thomas often referred to as the doubting Thomas?

Answer 1

Some of the disciples saw Jesus after he rose form the dead. They went back and told the others. But Thomas said that unless he put his hand into the wound, he would not believe. In other words, he doubted what the disciples told them. Later he did believe.

Answer 2

This tradition comes from John's Gospel, where Thomas is shown to hold doubts about Jesus, when all the other disciples show unquestioning faith. Elaine Pagels (The Secret Gospel of Thomas) sees a principal objective of John to refute the beliefs of the Thomas Christians early in the second century. Only John presents a challenging and critical portrait of the disciple he calls 'Thomas, the one called Didymus'.

The most well known demonstration of Thomas' lack of faith occurs in John chapter 20, on the evening of the Resurrection. Luke's Gospel had the risen Jesus appear to the remaining eleven disciples at their evening meal, and show his wounds. But in a parallel passage, John had Thomas absent at this time and, with only ten disciples, Jesus breathed on them and gave them the Holy Ghost. On hearing of this, Thomas expressed strong scepticism. He was present when Jesus returned a week later, and now believed what he could see, but of course he had missed out on the Holy Spirit (In a separate tradition, Acts of the Apostles has all the disciples receive the Holy Spirit on the day of Pentecost).
Other examples of Thomas having doubts about Jesus include: John 11:16, where Thomas did not believe Jesus would raise Lazarus; John 14:3-6, and again in 14:22, when Thomas showed doubts about what Jesus said to them.