Why is Hamlet mad at Ophelia?
In the third act of Shakespeare's Hamlet, Ophelia goes to Hamlet to return "remembrances" that he had given her when he was wooing her. He becomes upset with her because she is completely rejecting him by returning his gifts, but he also knows that she is acting under the direction of her father to spy on him. He asks her if she is honest, as if to also ask if she is being deceitful at that very moment. This so happens to be the case because she knows that Claudius and Polonius are watching the couple as the scene plays out. The uncle and father want to see how Hamlet reacts to Ophelia and to find out if he is really going crazy.
Hamlet becomes emotionally charged because he truly loves Ophelia, but he can't do anything about that at the moment because he is pledged to avenge his father's death. He becomes very frustrated that on top of having to decide what to do about his murderous uncle, he now has to deal with Polonius manipulating his love to go against him. He responds angrily by saying the following:
"I have heard of your paintings, too, well enough. God hath given you one face, and you make yourselves another. You jig, you amble, and you lisp, and nickname God's creatures, and make your wantonness your ignorance. Go to, I'll no more on't. It hath made me mad. I say we will have no more marriages. Those that are married already—all but one—shall live. The rest shall keep as they are. To a nunnery, go" (III.i.142-148).
The above passage also shows that Hamlet has lost faith in the sanctity of marriage, due to the fact that his mother betrayed his father to marry his uncle. And now, the woman he would have married has betrayed him by listening to her father rather than staying true to him. (This should be no surprise, though, for daughters were supposed to obey their fathers completely until they were married. Ophelia acts as the dutiful daughter at her father's bidding during this scene and by rejecting Hamlet.) Unfortunately, the conflict intensifies at this point because Hamlet realizes that he has lost his trust in Ophelia along with the trust he has already lost in his mother.