It is one thing to look at characters in the Bible. It is perplexing to see things as we think they are, and then hold that image up against the promises of God. We are not the first to be surprised by the possibilities which God presents. Nothing in Mary's experience could have prepared her for the shocking reality of the angel standing in front of her. An encounter with a message from God is an awesome thing.
Fear is often the initial response in the face of the unexpected.
Then if one comes to believe that the contact is of God, the mind kicks in and wants explanations. Mary asks when she is told that God's son will be carried within her. On the face of it, it does seem impossible. This doesn't fit with our understanding of how things normally work. It seems impossible that Elizabeth, known to be barren, could carry John in her womb.