It's a challenge to find many logical fallacies in the short story because its subject matter strikes fear in the heart of the reader.  The idea of child abduction and murder is one of the most horrifying conditions of the modern setting.  The fact that our social order has to deal with it is something that is irrational both in its presence and our reaction to it.  However, if one were divorce the emotional content from the setting, a logical fallacy would be how Arnold Friend knows everything about Connie.  The manner in which it is shown in the story is that he is the absolute authority on Connie and while he might have pursued her in what could have been an early example of "stalking," it is not made entirely clear how he has able to ascertain so much about her, thereby increasing his hold over her.  If this was going to be stretched, perhaps another logical fallacy would be how Connie simply resigns herself to going with him.  It is seen as a sacrifice and helps to develop the characterization as well as the thematic ideas of the story, but it is illogical that Connie, who is seen as shallow in her pursuit of the life of the self- interested teen, would simply capitulate and go.  The pangs of family loyalty were never a part of her character, and from a logical standpoint, it does not seem like they would suddenly develop now, at that moment when self- interest means life or death.  However, all of this is simply analytical.  These assertions do not take from the story's meaning or power.  They do not even remotely detract from its purpose and its relevance.  Finally, these ideas do not remove the validity of the story and what it seeks to say about human beings, the world in which they live, and how we, as the reader, interpret such events in our own contexts.