Do you think Dawn was bound to become a sociopath/psychopath? ?
Let's ignore Dawn's tragic suicide from Palindromes and pretend that she didn't die:
What IF Dawn grew up to be an adult and actually becomes a full fledged sociopath or psychopath?
To the point where she would become a dangerous, angry serial killer.
There were numerous evidence that Dawn displays signs and symptoms of an antisocial person:
She has no empathy - Dawn treated her best friend Ralphie (the ONE person that always treated her with kindness) like crap and felt no remorse about it. She also felt no remorse about having Missy go missing. Yes, she was trying to go look for her, but if you pay attention to her dream about being loved for finding Missy, you would understand her motive. She's just that selfish and thought that finding Missy would make her feel loved and popular (example of narcissistic personality disorder). When Dawn was walking home, she hit a ball out of a kid's hand for no reason. Again, she felt no remorse.
She's a liar - Dawn lied to the police about giving Missy the note, when she didn't. She lied to Missy about not sawing her doll's head off.
Destructive behavior - Dawn sawing missy's doll's head off. Dawn smashing her parents' home movie video of their anniversary with a hammer. Dawn standing by Missy's bed holding the hammer as if she was going to kill her.