Mm, the idea of "family" is something that's made up by people. Different groups of people have defined it different ways across different places and times, so it's impossible to give a single definition and decide that one is the "point." Um, for example... It used to be that married couples would have lots and lots of children! But it wasn't just to have children, necessarily—it was so they would have a lot of helpers to work on the lands they owned, and because it was common for kids to die before adulthood back then. So if you could ask a parent from back then about what the purpose behind having a family was, you'd probably get a really different answer than if you asked a parent from nowadays.

Anyway, for magi, bonds aren't the point at all. It's about carrying on a bloodline, to continue the work your ancestors started. Family is a tool, so it doesn't matter if your kids like or even love you. And because of that, even when you're taught that you shouldn't care about other people, you're still expected to function as one of your family's pieces. There's no point to having a useless tool, right?