Mary was troubled by the angel's greeting (Luke 1:28-29) Perhaps she thought she was crazy or that God spoke only to men. The angel's explanation should have troubled her more, but she accepted it with the faith of a child and was willing to accept God's plan for her. (Luke 1:38)
This passage also shows God's ability to put people in places where He wants them to be and to give whatever is needed for the task--a virgin and an old lady are both having babies according to His will. If I am to be like them, I must give Him the credit as Elizabeth did (1:25) and accept the appointment as Mary did (1:38).