Exactly, Jennifer.

Because she believes those people will try to take the monster away from her or harm it in some way. She's trying to protect it. She mentions this towards the end of the film, after her husband learns of the monster.

that's a great question. I am trying to think symbolically why Anna kills everyone who witnesses her in her most vulnerable/honest/atavistic self, and I assume it's because she is fighting against it. Anna is wanting to rid herself of her desires, maybe out of guilt or fear, or anger at her tragic indecision to wholly embrace one identity or "the other."