The family projection process is a fancy way of saying that a parent's problems are passed to the child.
If a parent is anxious, then the child becomes anxious, and then the parent focuses on the fact that the child is anxious and tries to fix the child. Which leads the child to believe there is something wrong with them.
A parent who is a perfectionist gets upset when things aren't perfect. A child may pick up on the parent's anxiety and may feel they have to be perfect as part of caretaking their parent. The child develops anxiety because they are scared to fail and let down their parent. The parent sees anxiety in their child has and feels they need to fix it. This puts more pressure on the child to 'be fixed' because they want to make their parent happy, which just causes more anxiety.
This leads to a vicious cycle. It is driven by a parent's lower level of differentiation and is often exacerbated by emotional triangles.