Prove whether or not you believe Hamlet loves Ophelia, or if she is merely a pawn in his lies and nothing else. If he loves her, why does he treat her the way he does? If not, what does his treatment of her say about him, morally? Do you believe he regrets his actions toward her, or that he is too far gone to recognize the inhumanity of how he treats her? To what extent do you blame him for his treatment of her, and to what extent do you blame other outside forces? Lastly, why do you believe this relationship is important for understanding Hamlet as a tragic protagonist? How would his life have been different if he had embraced Ophelia?

The discussion of whether Hamlet truly loved Ophelia is a timeless and complicated question. Love is never as simple and straightforward as we see in modern romantic movies when it comes to Shakespeare, and this intrigue is what adds to suspense and captivation of the tale between Ophelia and Hamlet.
In my opinion, Hamlet loves Ophelia, but the circumstances of Hamlet’s life when his father is murdered makes his love for her difficult. When Ophelia dies, Hamlet has absolutely nothing to gain anymore, but he is still compelled to go to her grave and leaves his hiding place, which leaves him vulnerable by showing himself to all of the people there. This action shows that he is acting out of passion and love. It does not show a conniving person, but someone acting out of love. It is almost as though he has no control over his passion and emotions. He then declares his love for Ophelia to her brother and his family.
He says:
I loved Ophelia. Forty thousand brothers could not with all their quantity of love make up my sum. (247-249)
Here he declares that he loved her much more than even forty thousand brothers could. This declaration comes at a time that shows absolutely no motive other than his need to express his love for her. It also shows complete grief at the loss of her. He even admits that if he could, he would be buried with her. Only a man in love with nothing left to lose would make such claims.
Now, this love he shows for her can be very confusing. This is because he treated her so terribly. Why did he do this? Why would a man in love treat the woman he cares for terribly? One explanation could be that Ophelia broke his heart earlier. If he did, indeed, care for her, when she broke off the relationship, he would have been very hurt. He could have spoken so harshly to her out of a wounded heart and hurt. It could also be that he wished to keep up his appearance of being insane. Maybe he was even trying to protect her from the murderous grips of his uncle. A man in love will go to great lengths to protect the object of his affection.
Hamlet is sometimes despised, because he is known for taking down and destroying many characters and Ophelia is one of them. His treacherous behavior doesn’t seem to be linked directly only to Ophelia, but to many others, so in a sense, his cruelty isn’t necessarily personal.
Ophelia could never really act on her love to Hamlet, because she chose to obey her father’s wishes and ended the relationship. Parents had a very big role in romantic relationships during this time, and Ophelia’s obedience left Hamlet out in the cold.
In conclusion, Hamlet was far from an angel. He did not show Ophelia the love that allows the reader to inconclusively sense his undying passion. But the times were difficult, and Ophelia had to follow her families orders. Both Ophelia and Hamlet were in difficult situations and Hamlet chose to treat Ophelia unkind. However, when she dies, it seems that the true nature of his love for her comes to full surface. He publically displays his love for her when there is nothing he can do about it. This displays the true complicated and tragic nature of love and the display of the human psyche in Shakespeare’s novels.

I believe Hamlet truly does love Ophelia as much as he can do under the circumstances of his life after his father's murder. After her death, when he has absolutely nothing to gain, he seems compelled to rush forward into her grave from his hiding place at the cemetery—revealing himself to everyone there—as though he has no control over his own actions. He then declares to Laertes, Ophelia's brother, and his own family,

I loved Ophelia. Forty thousand brothersCould not with all their quantity of loveMake up my sum. What wilt thou do for her? (5.1.247-249)

He swears that he loved her more than tens of thousands of brothers could do, and, again, it's pretty difficult to come up with a truly plausible motive for this behavior other than overwhelming grief. He claims that he would be buried with her if he could.
Perhaps Hamlet treated Ophelia so terribly because she broke his heart. If we assume that he did, in fact, love her, then her breaking off their relationship—when she had, apparently, given him indication that she loved him too—would have wounded him greatly. Maybe he spoke to her so cruelly at times because he was angry at her, perhaps it was all to keep up his appearance of insanity, or perhaps it was because he was trying to protect her from his uncle's murderous machinations.
One reason that Hamlet is such a tragic character is that he takes so many other characters down with him, Ophelia being the most innocent of all. She was only trying to be happy, and then her father bid her destroy her relationship and her ex began (she believes) to lose his mind and treat her cruelly. Perhaps she never would have gone mad herself if it were not for the difficult position in which the men in her life put her. Hamlet in many ways seems responsible for her demise. Unfortunately, he did not really have the option to "embrace her" because she obeyed her father's commands to end that relationship. Had he tried, however, it seems likely that no one would have objected to their relationship after all. Gertrude at one point tells her,

Ophelia, I do wish That your good beauties be the happy causeOf Hamlet's wildness. So shall I hope your virtuesWill bring him to his wonted way again. (3.1.39-42)

Gertrude, at least, would not have stood in their way.