Miranda falls instantly in love with Ferdinand. Miranda has been isolated on the island for twelve years with only her father, Ariel, and Caliban for company.
It is no wonder that she would quickly fall for someone that is not a relative, a spirit (although she mistakenly takes Ferdinand for one initially), or a beast(as she regards Caliban-and rightfully so).
Ferdinand will have to prove his worthiness to Prospero in order to win acceptance from him.
Ariel isnt her father.....