Because in America? If your priority if caring for your family, you are fucked. Nothing in this country facilitates that. It's the only allegedly civilized nation that doesn't even require paid maternity leave. Participating in society requires money, for most people that requires working for someone else, and jobs now demand all of a person's reliability. How easy is it for you to take time off if a relative is sick? Or attend family events? Or make a date with someone to do things together? Or take someone to an appointment? It's not. It's a nightmare.
So much of society undermines our ability to take care of the people we love -- or even find time to form such deep relationships in the first place. Plus, ties have fragmented from clan to nuclear family and now down to ones and twos. Fewer families stick together long term, instead fraying over a mess of unwed couples breaking up, married couples divorcing, people remarrying several times, and so on. Fewer young people are marrying at all. They're having fewer children, which not only means fewer siblings now but also fewer aunts and uncles and cousins in the future.
Many people are anxious, depressed, lonely, and just generally miserable. Because we've built a society that does a really shitty job of meeting our needs.
Here's the thing: if caring for family is a priority, not merely a wish, that means you have to put it above everything else, somehow. That weird thing the Amish do with rejecting technology? The motivation behind it is community ties. They simply won't tolerate anything that breaks up families or communities. They've given up one hell of a lot to pursue that priority ... but they absolutely have the thing they want the most. Which rather puts them ahead of most other subcultures in America today.
If we want to fix the problems America faces, we need to look at meeting people's needs better. Family is a big part of that. I'll add that it doesn't have to be defined by blood or marriage or whatever, just the people who mean a lot to each other.