In Brave New World, why are family words like father and mother viewed as obscene?
In Brave New World, the World State has created stability by genetically engineering its citizens to be happy with who they are and what they do. People are not born, they are decanted in hatcheries; and medically and psychologically manipulated so that they have just the right intelligence, strength, and attractiveness to fill the social and economic positions that will need to be filled.
These decanted children are raised and indoctrinated in conditioning centers so that, by the time they are old enough to work, their only ambitions are to perform the tasks for the positions they were raised to fill. Their loyalty is to the state and to continued community and stability. Family and its language are obsolete concepts.
But it's more sinister than simple obsolescence. The World State maintains stability by obliterating individual personality. People of the same caste are largely identical by design. Very few personality traits are left to chance, and people are encouraged (through promiscuity) not to form strong bonds with other individuals.
There is no stronger bond than family, and family is a major factor in self-identification. And what better way to eliminate family than to make it a dirty word?
So in Brave New World, we see a reversal from what we know today. People are raised to think of the language of sexual promiscuity is normal and expected and accepted, while the language of the family is obscene. This manipulation of the language is just another way that the World State controls citizens and maintains stability.