In order to reestablish their structural organization, the pathology of the narcissistic/(borderline) parent must externalize onto you their own primal self-inadequacy and fears of abandonment. They must make you the inadequate and abandoned person, and they can accomplish this through the child.
By inducing the child into rejecting you, the child’s rejection of you defines YOU as the inadequate parent (person) who is being rejected (abandoned) for YOUR inadequacy as a parent (person).
The child’s rejection of you allows the narcissistic/(borderline) parent to restore their narcissistic defense against the experience of primal self-inadequacy and fears of abandonment that had collapsed with the divorce. The child’s rejection of you allows them to psychologically expel (project) their core beliefs onto you; you’re the inadequate person (parent), and you are being abandoned for your fundamental inadequacy.