I had read Bateson's work years ago and found it persuasive. I also found R. D. Laing's quite different explanation of society's role in generating schizophrenia to be persuasive as well.
I do agree that whoever (regardless of gender) takes on the role that we call mothering may be a key influence on the child's development, but now I believe that both (or multiple, in an extended family) parents set up scripts for their children, and the purpose of these scripts (probably not a conscious purpose) is to turn the child into the parents, to keep the child from achieving autonomy--no matter how old the child becomes. And most likely this kind of scriptwriting was instilled in the parents by their parents, etc. These scripts are augmented by larger social units, especially institutional education, institutional politics, and institutional religion. Ultimately, the conflict between the child's need for autonomy and the parental / social drive to curtail growth and independence will create major problems for the child. Schizophrenia? Probably, but even in less severe cases, the conflict may cause damage at any point in the child's (adult's) life, even after the parents are no longer living.