Why does Polonius have the right to tell Ophelia that he doesn't want her to see Hamlet anymore?

In short, Polonius has the right to tell Ophelia that she must break off her relationship with Hamlet and not see him anymore because Polonius is her father. As a young woman during this time, Ophelia has an obligation to obey her father, and, then, once she is married, she will have a similar obligation to obey her husband. Because Ophelia is unmarried, her father is particularly concerned about her virtue; she must remain a virgin until she is married so that someone will marry her. Polonius is afraid that Ophelia might, mistaking Hamlet's lust for love, sleep with him, and then her virtue will be lost along with her prospects for making a good match. He feels certain that, even if Hamlet does love her—though he doesn't think this is the case—Hamlet is not at liberty to marry her, because he is royal and Ophelia is not. Since they can never marry, Polonius thinks it's best to break them up now and protect his daughter.