What is the Two Minutes Hate? Why does the Party try to destroy loving relationships? Why would they do this?

It is no coincidence that the object of hatred, the face of Emmanuel Goldstein, the "primal traitor, the earliest defiler of the Party's purity," appears at each Two Minute Hate session.  For the surname is Jewish, thus suggesting the object of Nazi hatred around which Hitler was able to lead masses of people. Knowing that hatred is, perhaps, the most virulent of all emotions that will unite people, Hitler capitalized on the sentiments of the German people that the Jews were responsible for the economic collapse of their country.  The Russians, too, shared this hatred of the Jew as many were killed during the time of the czars and Stalin, as well. (Some elements of the plot of "1984" parallel the rise of Stalin and later Communism.)

In "1984," the characters immediately react when they see the face of Goldstein whose first name, is, of all things, Emmanuel. The paradox of having a name that means "Christ" or "Savior" cannot be missed, either, since Goldstein is anything but the savior of the people of "1984" because he is defiled for his denouncement of the Party:

an attack so exaggerated and perverse that a child should have been able to see through it, and yet just plausible enough to fill one with an alarmed feeling that other people, less level-headed than oneself, might be taken in by it.

The Two Minute Hate exploits the herd syndrome of people, too, as when people begin shouting their hatred, Winston finds it "impossible to avoid joining in."  So, while the people are repulsed by the "sheeplike voice" and appearance of Goldstein, they become like sheep in their unified reactions.

It was even possible, at moments, to switch one's hatred this way or that by a voluntary act.  Suddenly, by the sort of violent effort with which one wrenches one's head away from the pillow in a nightmare, Winston succeeded in transferring his hatred from the face on the screen to the dark-haired girl behind him.

The Two Minute Hate works by means of the herd syndrome of people; many are very much like sheep, simply following the lead of others and reacting viscerally rather than intelligently to subliminal suggestions and rumors.  Orwell's portrayal of people in "1984" protrays people who are losing their individuality and, thus, their human qualities.