Family has supreme importance to the Chinese. Filial piety is almost a religion to them. The highest virtue of Confucianism is ancestor worship and respect for parents.
The fourth of the Ten Commandments says to "honor thy father and thy mother". To Chinese, Americans do not follow that at all. Chinese children commonly support their parents thru old age, while American children abandon their parents.
However commendable these Chinese family values are, they are very different from American values. Chinese respect for elders makes them very authoritarian. They tend to be very fatalistic based on the status quo and on education credentials. Americans are much more individualistic, democratic, and scientific.
Immigrants from India also have very strong family bonds. Traditionally, their occupational choices are limited by the caste that they are born into. Fortunately they do not bring their caste system into the USA. Children are reared by an extended family who mold their personalities and eventually arrange marriage.
Many other foreign cultures are big believers in cousin marriage. As a result they are divided into clans that seem like huge extended families, and there are strong allegiances within the clan. Again, these bonds may seem like strong family values, but they are not American family values.
We are getting most of our immigrants (legal and illegal) from Mexico. They are mostly Catholic with strong family bonds, but as Heather MacDonald explains:
The myth of the redemptive Hispanic is finally cracking. For years, conservative open-borders advocates have touted Hispanic “family values” as a prime reason to increase immigration. Hispanic immigrants, these conservatives say, will save America from itself. ...
The truth is now supplanting the fiction. Last Friday, the New York Times ran an editorial, “Young Latinas and a Cry for Help,” that laid out the real state of the Hispanic family. A quarter of all Latinas are mothers by the age of 20, few of them married, reported the Times. This out-of-wedlock teen-birth rate is three times that of white teens, and significantly more than that of blacks as well. The Hispanic dropout rate is also the highest in the country — the Manhattan Institute’s Jay Greene puts it at 47 percent.
There is simply no way to square the facts about Hispanic family breakdown with the myth of the redemptive Hispanic. Talk to any social worker and she will tell you that illegitimacy has become completely normalized among her Hispanic clients. ... And they have no qualms about hooking their daughter and grandchildren into the public-benefits apparatus: “It’s now culturally OK for that population to be served by the welfare system,” says a case manager in a Santa Ana, Calif., home for teen mothers.
There are many exceptions to these cultural stereotypes, of course. And there are other considerations that go into immigration policy. But the point here is that the immigration of the last few decades has brought a population with a notion of family that is distinctly contrary to the traditional American family, as acknowledged in this NY Times story about the demise of the Ozzie and Harriet archetype.