Note: The abolition of the family is one of four major aspects of socialism. That is because "abolition" implies in the minds of many people a gradual, somewhat benign cessation of family formation or of the existence of families (e.g.: "non-fault" divorce). In reality, "abolition" is not quite the correct term and the term "destruction of the family" more accurately describes the circumstances.
No-fault divorce is hardly ever seen as being what its name identifies. Almost invariably (but wrongly in about half of the cases) the man is seen as the guilty party at fault and as deserving to be sentenced to life-long punishment for having dared to be married. Moreover, it can hardly be seen as a benign process if people are so afraid of the liabilities incurred on account of being punished for wanting to form a family that they forego that pleasure to the extent that their deliberate resolve not to have a family and not even children causes their nations to die out. That is the case with all developed nations. (See Demographic Winter)
At this website, the term "abolition of the family" is used infrequently and the term "destruction of the family" is used far more frequently. You can perform a site-specific search at the website of Fathers to find instances of web pages that refer to or discuss the destruction of the family.