Julia and Winston are attracted to one another. The party is in charge of approving all relationships, and they would not allow one if the couple appeared to be attracted to one another. Sex is meant for procreational purposes only. Once a couple is allowed to marry, they are only supposed to engage in sex to create children. If the marriage has no children, the couples are encouraged to live apart. There is no divorce. By pursuing a relationship based on attraction and sex, Julia and Winston are going against the Party.
The Party's purpose in controlling relationships is to discourage loyalty to any other person or group.
The Party, in George Orwell's classic depiction of a futuristic dystopian society, 1984, seeks absolute control over society. That control extends to the thought processes of each member of this society, known as Oceana. This is, after all, the story that introduced into the English language the phrase "Thought Police." Early in the opening chapter of 1984, Orwell's protagonist, Winston Smith, describes the oppressive environment in which he, and the rest of the citizens of Oceana, function. The roving police patrols, he notes, do not bother him that much; rather, it is the Thought Police that are the constant concern: "Only the Thought Police mattered." In Orwell's dystopian, totalitarian society, it is not enough to control people's actions; as important is the ability to control their minds, and this is accomplished through an ubiquitous system of political indoctrination.
Among the prohibitions on personal conduct that dictate how the citizens of Oceana live their lives is the notion of personal relationships not approved by the Party. Sexual relationships, in particular, are strictly regulated for the purpose of procreation. Hence, the "Junior Anti-Sex League" sash wrapped around the waist of the "bold-looking girl," the sash representing, perhaps, the chastity belts of an earlier age. The Party's position on personal relationships and on the role of sex in Oceana is described in Chapter 6:
The aim of the Party was not merely to prevent men and women from forming loyalties which it might not be able to control. Its real, undeclared purpose was to remove all pleasure from the sexual act. Not love so much as eroticism was the enemy, inside marriage as well as outside it. All marriages between Party members had to be approved by a committee appointed for the purpose, and—though the principle was never clearly stated—permission was always refused if the couple concerned gave the impression of being physically attracted to one another. The only recognized purpose of marriage was to beget children for the service of the Party. Sexual intercourse was to be looked on as a slightly disgusting minor operation, like having an enema.
This lengthy passage from 1984 pretty much sums up the situation. Winston and Julia's relationship is a direct challenge to the Party's control. In totalitarian societies—and Orwell famously modeled his dystopian society after Stalin's Russia—independent thoughts and actions are interpreted as hostile acts, punishable by long prison terms accompanied by physical and mental torture. In fact, the Soviet Union was well-known for punishing dissidents with compulsory psychiatric treatment. The belief, given the seemingly omnipotent nature of the regime's security structures, was that one had to literally be insane to oppose the Communist Party. Orwell simply borrowed from and expanded upon the system that governed the former Soviet Union for 80 years.