Families are dependent on each other for multiple forms of support.
Families are dependent on each other for physical, emotional, and economic support. Parents support their children by providing them food, shelter, and clothing during their early years of life. In many cultures, as children get older, they then take care of their parents and offer them food, shelter, and clothing in return.  Families also provide each other with physical support. If a child or parent is hurt, the other one will take them to the hospital or provide medical aid. Without that support and oversight, their lives could end.  Families who have heavy patterns of dependency often pass those on to their children.  Cycles of family dependency are very difficult to break.  Children who have parents that can't provide, because of economic issues, substance abuse, abandonment, or other reasons, have a significantly harder time succeeding in life. A healthy family life and the ability to be dependent at a young age is important for development. Family is dependent because that is the most successful and normative way in the modern world for families and individuals to succeed.
Family is not dependency. In fact, family teaches a person to be an individual. Parents teach children to do their own work, do their own chores, and eventually, live on their own. Families give each other the tools to succeed but are not dependent on each other to do so.  Modern families are highly independent, with families living far away from each other than ever.  Families are also more broken up. Parents are more likely to be divorced and children are more likely to be more dependent as a result. With families being more separated, they are also less dependent. Family is not dependency; rather, family teaches children to be independent and go out into the world on their own.
Rejecting the premises