There are many topics to choose from in interpreting this story. It is based on an actual serial killer who preyed on teenage girls in Arizona in the 1960s. Using this as background information, it would be easy to show how it is a fictional interpretation of real historical events. But, it would be more interesting to consider metaphorical and allegorical interpretations of the story.
Connie is a typical teenager. She goes to the mall with friends and is primarily interested in superficial things: how she looks, the latest popular music, and rebelling against her parents for any reason. Initially, she is portrayed as a superficial girl. She wants to be noticed and gazed at by other boys. She wants boys to tell her that she's pretty. We can blame this selfishness on Connie's vanity but we could also blame a society that has conditioned her to desire to be have this way. Society tells her to look pretty; otherwise, boys won't like her. So, despite her seemingly selfish behavior, she's also simply trying to be acknowledged by her male peers. As of yet, she doesn't really know another way to be.
In short, Connie is superficial but she's also naive and doesn't yet understand her place (or woman's place) in the world. With all of that being said, you might go with a thesis that argues that when Connie walks out that door, she has awakened from that teenage, superficial daze into the harsh world of adult men and women. Innocence gone, she enters a world where some men still wield power over women. She enters into this unjust world suddenly. The potential violence implied by Friend's behavior underscores how sudden this awakening is. It is a harsh, unfair awakening. This is the argument: a harsh, unfair awakening into an unfair world.
Now, based on the historical background mentioned earlier, it might sadly be the case that Connie is to be kidnapped, murdered, etc. But in addition to that Realist possibility, let's run with the metaphorical interpretation which is that Connie's innocence is lost. By leaving her house in this symbolic way, she enters into a world where women inevitably succumb to the desires of men. It is a world, unfortunately, where men are understood as predators and women are understood as prey. At this moment, Connie is alone in facing this. If only she had some answers, some belief system (such as feminism), then maybe she could break the cycle of women entering a world of men objectifying and dominating women.