It was basically that Freud was suffering from his own unresolved childhood traumas and avoiding them forced him to narrate his theories from the perspective that the parent was innocent and the child was guilty, especially when discussing the treatment of seemingly misbehaved children.

Unfortunately, this continued to be the main perspective in psychoanalysis and child development until the late 1970's/early 1980's

She gives an explanation in its simplest form in a 1987 interview with OMNI Publications International:

Traditional analysis, says Miller, duplicates the parent-child relationship with the conventional analyst in the position of power. [...] The child undergoes a long inner struggle “between the fear of losing the person he loves if he remains true to himself, and panic at the prospect of losing himself if he has to deny who he is. A child cannot resolve a conflict of this nature and is forced to conform because he cannot survive by himself. Therapy should not repeat this condition.”

fascinating read if anyone's interested, especially when she describes the first time she discussed this to a conference of psychoanalysts:

http://www.alice-miller.com/en/the-feeling-child/