Why is the Church called the Mystical Body of Christ?
St. Paul refers to the Church as the body of Christ repeatedly (cf. I Corinthians 12:12), but in order to understand why he does so, as well as its significance, we need to focus on Paul's conversion (Acts 9:1-6).
"Now as he journeyed he approached Damascus, and suddenly a light from heaven flashed about him. And he fell to the ground and heard a voice saying to him, 'Saul, Saul, why do you persecute me?' And he said, 'Who are you, Lord?' And he said, 'I am Jesus, whom you are persecuting.'" (Acts 9:3-5).
This encounter with Jesus apparently formed St. Paul's theology on the Church. Paul saw the Church as a divine institution, with Jesus as its head and we as its members. Indeed, Paul saw that Jesus Christ and His Church are one and the same. Notice that Jesus did not ask, "Why do you persecute my followers?" or "Why do you persecute my Church?" He asked, "Why do you persecute me?"
Jesus had ascended into heaven a long time before St. Paul met Jesus on the road to Damascus, so he could not have been persecuting Jesus. The persecution was of His followers. But that isn't what Jesus says. Christ's words are clearly indicative that to persecute His followers is to persecute Him. This is why St. Paul taught that we are the members of the body of Christ—the Church—and He is its head. You cannot persecute any one part of the body without the entire body suffering. Paul understood that Jesus and His Church are one.