When one parent works hard (and seems to succeed) in alienating the child from the parent, on the other hand, it may be hard for the parent to feel that s/he is a part of the child’s equation, and conflate his/her estrangement with his need to contribute to this ungrateful child’s education. S/he may feel to some extent that the child has been “lost” already. Not the right “math” in many people’s opinion, but it is human nature.
A good lesson in not using the children against the “ex.” Both parents are really needed by the child.
In the end the child is the loser, and is a victim of forces beyond his/her control. Each child in this sort of situation probably very much loves both parents despite how she acts, and will find ways to show it as she matures.