What would be a good argument against the fairy tale aspects portrayed in "Where Are You Going? Where Have You Been?" by Joyce Carol Oates?

Perhaps the most obvious way in which this story could be said to portray fairy tale elements is in the way that Connie responds to Arnold Friend. He is a sort of "Big Bad Wolf" character in that he is rather obviously not a wholesome or kind person, but he has a kind of charm and is rather seductive. In fairy tales, the Big Bad Wolf is a sort of archetype who represents aggressive male sexuality; he is usually contrasted with a more innocent character such as Little Red Riding Hood. The red cape and the color red in general can be seen symbolically on several levels: it symbolizes the blood of menstruation, a sign of sexual maturity, or of loss of virginity, or of lust.

Red Riding Hood is manipulated by the Big Bad Wolf and brings harm upon her grandmother; in Oates' story, the "wolf" (Friend) threatens Connie's family's safety, so she agrees to go with him. Connie is also somewhat sexually attracted to Arnold Friend, even as she is repulsed by him; the text refers again and again to her heart racing and her feelings of helplessness, a mixture of fear and arousal. She wants to run away, but she can't say no. He wears her down with talking and she can't resist any longer.

In the end, her choice to go with him may be seen as a rite of passage, in which she says goodbye to the innocence of her childhood and the safety of the family life she has known. It is not clear in the end what Connie's fate is, but the last few lines of the story do suggest a hint of dread:  

She watched herself push the door slowly open as if she were back safe somewhere in the other doorway, watching this body and this head of long hair moving out into the sunlight where Arnold Friend waited.

"My sweet little blue-eyed girl," he said in a half-sung sigh that had nothing to do with her brown eyes but was taken up just the same by the vast sunlit reaches of the land behind him and on all sides of him—so much land that Connie had never seen before and did not recognize except to know that she was going to it. 

She sees herself as if she is outside her own body, which may be a foreshadowing of her death. She also sees the land and knows she is "going to it," which may hint that she will wind up dead in the fields, possibly buried there.  In many fairy tales, the fate of the heroine is sometimes not a happy one. The ending here is ambiguous, but the story's depiction of Arnold Friend suggests a predator determined to make a victim of Connie.