Why did Jesus call Himself the Good Shepherd?

Read John 10.

In the last verse of chapter 9, Jesus pronounced upon some of the Pharisees that "your guilt remains."  Why?  What had they done wrong?  In their pride, they refused to admit their spiritual blindness.  The Messiah stood in front of them, but they rejected His claims of being the Christ (v.25) and God (v.33).  But Jesus did not stop there.  He referred to them here as:
1. Thieves, because they tried to live and teach the people "another way" to please God and enter His kingdom.  
2. Robbers, because they hijacked what belonged to God for their own purposes.
3. Hired hands, because they had a positions and religious jobs but not a heart committed to God or the people.

The contrast Jesus made was blunt and clear.  Twice in this chapter He used the "I am" phrase.  This hearkens back to Moses' encounter with Jehovah, the I AM, at the burning bush.

"I am the door of the sheep." (v.7)
When the sheep hear their shepherd's voice they come (v.3) and gather in a safe place.  The shepherd makes sure that all His sheep are accounted for and no others have strayed into his flock.  Then, he stations himself at the entrance of the gathered place for security of the sheep inside and to protection from the outside.

Jesus will later state, "I am the way, the truth and the life.  No one comes to the Father except through me. (John 14:6)  There are not two ways to please God and get to heaven.  Everyone must come through the one and only "door".

"I am the good shepherd." (vv.11 and 14)
In times of danger, as when a wolf attacks, the hired hands will not stand, do what is right, and fight.  They will run and protect themselves instead.  But "the good shepherd lays down his life for the sheep."  After using this analogy for a while, Jesus began to pull back the veil and reveal that He was actually referring to Himself.  Indeed, at the cross He will give His life for the redemption of His sheep "that I may take it up again" (v.17).  He looked forward to His own resurrection.

In addition, His provision for the sheep is "eternal life" (v.28a) and the security of the sheep for which He is responsible (vv.28b-29)

How loving and personal is this relationship between the Good Shepherd and His own!  "The sheep hear his voice and he calls his own sheep by name and leads them out." (v.3)  "My sheep hear my voice, and I know them, and they follow me." (v.27)

The comparison with Psalm 23, written by David (also a shepherd), is inescapable.  We are in the flock of God, cared for, and free from all fears (both now and forever) because "The LORD is my shepherd".