It's not so much the parenting classes that are a problem. I think all the parties have suggested them st one time or another. there are plenty of people who would like them or benefit from them.
The problem is offering parenting classes (and from the article relationship classes?) against a background of reduced legal aid, cuts to children's services and other state provision.
There is no parenting class that can feed the electricity metre when there just isn't enough money, force an absent father to take responsibility, help a family who need practical help because of illness or disability or help a child whose parents need a social worker, not a class.
However, framing the problem as feckless parents not knowing what's good for them is a great excuse to reduce services further.