yes, but he raped her because she was the only woman on the island. Who knows he could of loved her, but raped her because his mother was a witch named Sycorax and his father was the devil.
<- This is only partially right, as Caliban only tried to rape Miranda. He "seek[ed] to violate the honor of" ( I, 2, 347f) Miranda. Prospero stopped him from doing so.
In fact we do not know what this really means at all, but violating her honor is mostly interpreted as an attempted rape.
In my personal opinion, Caliban showing his affection towards Miranda would have been enough for him being accused of "violat[ing] the honor" of his masters daughter.
Also we cannot be sure, whether it is true, that the devil was Calibans father, as all we have is Prospero's account of what Ariel told him. Then where would Ariel now from? Ariel is not reliable, as he is talking of the witch who locked him in a tree, using magic. So saying that the witch Sycorax, Caliban's mother, had intercourse with the devil might just be a way of taking revenge on her as his enemy, by damaging her reputation. After all we don't know hardly anything about Sycorax at all.
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Miranda stands behind her father when she feels threatened by Caliban.
Caliban and Prospero hate each other because Caliban tried to sexually assault Miranda. Caliban has been taught how to speak and Caliban insulted his learned gift by just using it to insult Prospero and Miranda.
Caliban
The little monster in it is called, Caliban! He used to own the island.
Caliban is an outcast because he is a monsterlike being and not human.