The overwhelming force of this short and powerful narrative is to convey the experience of the doctor as something that is universal and deeply symbolic, that people of all ages, cultures and locations can relate to. What I find interesting about this short story is the way that Williams deliberately makes choices to try and convey the universaility of this experience, and his choice to refer to Mr. and Mrs. Olson as "the father" and "the mother" is definitely one of those choices, as this non-specific title detaches the narrative from being a specific case and allows this encounter to richly comment upon the ways in which even the most professional, intelligent and cultured of individuals can actually become overwhelmed with anger and a desire to cause violence and to force another person to submit to them.
The way in which the parents actually sit by passively whilst this occurs speaks volumes about our natural deference to authority. Note what the narrator says about them:
In the ensuing struggle they grew more and more abject, crushed, exhausted while she surely rose to magnificent heights of insane fury of effort bred of her terror of me.
Refering to them as "the father" and "the mother" therefore helps us to identify that this is just not a one-off and a case of two parents who cruelly stand by in ignorance whilst their daughter suffers an assault by a professional. Refering to them in such a way forces all parents to identify with the way in which the Olsons give in to the doctor and stand by meekly whilst their daughter suffers an assault that is tantamount to a rape.