Q. Why were the disciples afraid when Jesus appeared?
I’m assuming you mean to ask why the disciples were afraid when Jesus appeared to them after his resurrection. Luke explains in his gospel that “they were frightened and terrified because they thought they were seeing a ghost.” This was even after they’d gotten several independent reports that Jesus had risen from the dead, and even though he said to them, as soon as he arrived, “Peace be with you.” But fear is actually not an unusual reaction when someone in the Bible encounters a visitor from the spiritual world.
Gideon, for example, realizes that he’s been speaking with the angel of the Lord when the angel first sets on fire the food he has served him, just by touching it with tip of his staff, and then vanishes. God has to tell Gideon, “Peace! Do not be afraid. You are not going to die.”
Similarly, when a mighty angel appears to Daniel, he collapses on the ground, and then gets up “trembling.” (Understandably, because the angel’s “body was like topaz, his face like lightning, his eyes like flaming torches, his arms and legs like the gleam of burnished bronze, and his voice like the sound of a multitude.“) Daniel, too, is told, “Do not be afraid.”
When the angel of the Lord comes to tell Zechariah that his prayers have been answered and he and his wife are about to have a son (John the Baptist), even though this is good news, Zechariah is “startled and gripped with fear.” The angel reassures him, “Do not be afraid.”
During Jesus’ earthly ministry, he once walked on the Sea of Galilee to join the disciples in their boat far out on the water. Matthew records that “when the disciples saw him walking on the lake, they were terrified. ‘It’s a ghost,’ they said, and cried out in fear. But Jesus immediately said to them: ‘Take courage! It is I. Don’t be afraid.'”
And in the book of Revelation, John reports an experience similar to Daniel’s. He says that when he first saw Jesus in his exalted glory, “I fell at his feet as though dead. Then he placed his right hand on me and said: ‘Do not be afraid.‘”
I think it would only be natural for us humans to be startled and alarmed if we encountered a heavenly visitor. But it’s very encouraging to read in the Bible how God always reassures each frightened person by saying, “Don’t be afraid.” This helps us realize that whenever God steps into our lives—even if we don’t experience a supernatural appearance, but instead sense a divine hand at work in our circumstances—we can be confident that God has come to bring about good, not to harm us. So even if we’re startled (and maybe it’s good for us to be shaken up by the reality of spiritual things from time to time), we don’t need to be afraid.