What is attractive about shy girls?

Some men adore shy women, and they think that they are so cute. When a girl is a bit shy, it gives her an endearing quality that many men will find to be irresistible. Most shy girls are comfortable with letting a guy dictate the pace of a relationship, and they also let him plan the dates.

Why do shy girls reject guys they like?

Girls/women can like men as friends or humans without being romantically or sexually attracted to them. This means they may reject offers of romantic relationships or dates with a guy because while he is likeable as a person, he is not what they want as a romantic partner. Being shy or not has no bearing on this.