I've come across many people who believe in La Llorona, and one of the interesting differences in opinion that exists about her is that while some people believe she is evil to the core, other people believe she was merely a victim of her circumstances--forced (psychologically) in some way to kill her child.
I've had a challenging time trying to understand La Llorona. While I don't think that she is evil to the core, I do think that some of her actions have been and continue to be what many people would call "evil." Despite the motivations for these actions, she is (as we all are) still responible for what she does and how she moves through the world.
I believe that La Llorona is a victim in many ways. I think she drowned her child because she chose to accept what her environment imposed on her--which was to be a victim. And she continues to be a victim, as we see through her endless suffering. Society decided she--as a woman and a mother-- should be a victim and she agreed.
In the end, it seems most of us make the choice to be victims in a variety ways, and we aren't aware enough to realize it.
I think La Llorona has a lot to teach us about the pain of chosing to be a victim.