Now that's just straight-up bullshit. The family unit is a myth; common morals were never common.
Allow me to further explain.
The "family unit", aka "nuclear family" is a product of the 1950s boom era in Western society. Post WW2 economics gave most families the ability to live apart from family and friends in self-contained units. Previous to that, the norm was for brothers and sisters or parents and children to live together on farms or in apartments, especially with immigrant groups. During the 1950s and the proliferation of the middle class, individual siblings could afford to part from their families; the people who aged to retirement in the 1960s could afford to live on their pensions.
There are few statistics that show single-parent families are any less valuable than multiple parent ones excepting in time spent, and children that come from single-parent families aren't any more likely to commit crimes or go into drug abuse problems.
Now, we all like the idea of having a nuclear family, but that's just not going to happen for most of us. I came from one, and that makes me unique. My best friend has two adoptive siblings; my other best friend has a single mother who divorced young from his father.
The nuclear family has stopped being so important because it was a sham to begin with. Social convention kept relationships together that turned sour; divorce became the norm not because of feminism, but because 50% of marriages shouldn't continue. Children are pretty tough and sort it out most of the time.
And what's a common moral? Common morals change over time and adapt to circumstance. It was considered immoral in 1939 for a woman in the USA to show anything more than an ankle. By 1945 the knee was expected. By 1950, back to the bloody ankle. The same for today - morals (or at least social ones) fluctuate. We accept things today (divorce, same sex marriage, atheism) that were taboo topics when my parents were children. When my parents were children things were becoming acceptable that weren't acceptable when my grandparents were young (interracial marriage, a Catholic president, women working in greater numbers). And when THEY were young, we were discussing how society would die because of a new thing called "radio" bringing "music" into homes everywhere!
It's kinda the same old tone. Society is dying because of X and Y; but X and Y are always happening.