In Act I, Scene 2, there is an exchange between Prospero and Caliban which explains why Miranda sees Caliban as a "villain" and why Prospero treats him with extreme cruelty. Caliban complains that the island used to belong to him and his mother.
For I am all the subjects that you have,/ Which first was mine own king, and here you sty me/ In this hard rock, whiles you do keep from me/ The rest of the island.
Thou most lying slave,/ Whom stripes may move, not kindness! I have used thee,/ Filth as thou art, with human care, and lodged thee/ In mine own cell, till thou didst seek to violate/ The honour of my child.
O ho, O ho! would't have been done!/ Thous didst prevent me, I had peopled else/ This isle with Calibans.
In other words, Caliban tried to rape Miranda when she was younger. This is why she regards him as a villain, and why her father hates him so. Caliban doesn't even feel guilt over what he tried to do. He would do it again and again if he had the opportunity. Prospero has to watch his closely, and Miranda is afraid of him.