It has to do with the way the two different kind of dependents are defined.
For a qualifying child, the child can't provide more than half of their own support. It doesn't matter who does provide support (welfare, custodial parent, non-custodial parent, etc.) because residency is more important here. If the child supports themself (child actor, etc) they are not a dependent. Otherwise, your own child who lives with you is your dependent no matter who pays the bills.
For a qualifying relative, you must pay more than half the costs, no matter who pays the other half. That means the child can't support themself but is also means that you can't claim a dependent when someone else pays the support.
Qualifying relative is less-used and less understood. It applies to people like adult children who have aged out of being a qualifying child, and it applies to the children of your boy or girlfriend who live with you but you aren't married or their legal stepparent.
You personally have to support a qualifying relative dependent. But you can claim your own child as a qualifying child dependent as long as they live with you, even if someone else pays their expenses, and as long as they don't support themselves.
It's just the way the law is written.