In my opinion, Huxley is trying to say that monogamous relationships and romantic relationships in particular are a major part of what makes us human.
In the Brave New World, the relationship between sex and love or sex and any kind of emotion, really, has been removed. The idea of romantic love between two people has also been destroyed.
Huxley uses this (along with the drugs and the idea of kids being bottled and decanted and such) as one of the major symbols for how much this society has lost its humanity. By doing so, he is arguing that romantic relationships and emotions are an integral part of being human.
Brave New World is the antithesis of 1984 in terms of dystopia. Whereas 1984 has marriage, the state only condones it for the purpose of making children. So, marriage is a means to a political end. Husbands don't necessarily love their wives, and children don't necessarily love their parents. Remember, Parsons gets turned in to the thought police by his own children. In other words, marriage is not meant for ownlife, but to create children, who then, in turn, are used as fodder for the state (as spies or soldiers).
In Brave New World, the technology has been created to do away with the facade of marriage and relationships altogether. Married and dating, especially among the upper castes, is forbidden because it leads to monogamy and, therefore, to a disruption of the state's goals: identity, community, and stability.
More specifically, monogamous relationships lead to family values. These family values replace the loyalty to the state, or one's genetically engineered identity. If you are a junior DHC, like Henry Foster, you are effectively married to your caste, your identity, your job. To have a family or relationship is a grand, unneeded, unproductive distraction.
Since the goal of the World State is to replace family values and education with pleasure, sex is the obvious antidote for marriage. The sex in Brave New World is not sex for procreation; it is only for pleasure. Not only that, it is mixed with Soma (drugs) and used to replace religion.
Huxley even says the point of his dystopia is to account for "man's almost infinite appetite for distractions."
In his essay, "Amusing Ourselves to Death," Neil Postman writes:
In 1984, Huxley added, people are controlled by inflicting pain. In Brave New World, they are controlled by inflicting pleasure. In short, Orwell feared that what we hate will ruin us. Huxley feared that what we love will ruin us from the chapter “Media as Epistomology.”
In short, relationships and marriage are dangerous to dystopias and totalitarian governments because they are distractions that disrupt and threaten the rigid policies of the state.