I wouldn't put all the blame on the parents though certainly they should know better than this. In the past, I think kids like this would have been encouraged to try to accept their natural bodies. Now, the psychological paradigm is different.
Parents may have a child who doesn't feel comfortable in their bodies. I've even heard of cases where preschool aged children have tried to do things like cut their male organ off, saying it doesn't belong there, etc. Up to this point, it's probably not the parent's fault. There are probably different things that can cause this, but it may be out of the parent's control.
When the parents can't get the children to accept their bodies on their own, they turn, naturally, to psychologists and psychiatrists for help. These so-called professionals say, in a very authorative way, that the child has gender identity disorder and the treatment for it is not to encourage the child to accept their own body but to do the exact opposite, to feed in to the delusion and fantasy. Instead of making the disorder better, they go the opposite route, and convince the parents that they will be bad parents if they don't let their child surrender fully to their fantasies and disorder. They reinforce and encourage the sickness rather than making any attempt to make it better or to cure it. They have no interest in helping the child to have a normal body image and relationship with their true identity. Instead these sick so-called professionals want to encourage this child to go down a freakish path which almost guarantees sterility, social problems, etc.