She listened to David Bowie singing "putting out fire with gasoline." She didn't know the name of the song, but she took the words as prophetic. (29.121)
The title (Flickan Som Lekte Med Elden in Swedish) refers of course to Lisbeth Salander. From reading The Girl With the Dragon Tattoo, we know that Salander is pretty good at self-defense, but we didn't know that she holds in her heart a fierce and secret love for fire as an ultimate destructive force.
In this novel, we finally learn what "All The Evil" is: Salander tossing a firebomb into her father's car after he brutally beats up Salander's mother. This is the fiery act that results in Salander being committed to a psychiatric ward when she's twelve. In the Prologue, we see Salander fantasizing about burning up her sadistic psychiatrist, Peter Teleborian, while she's in the asylum.
In the present action of the novel, she only uses fire to light her cigarettes, though she certainly wants to burn her father and her half brother for good, and probably still has her fantasy of torching Teleborian. ("She saw him drenched with gasoline. She could actually feel the box of matches in her hand" (Prologue.31).) But, she doesn't do any of those things in the novel, in spite of David Bowie's prophecy.
We can also look at the fire in the title in a less literal way. We could look at Zala himself as fire – everybody involved with him gets burned. Plus, Zala (a high level Russian spy who defected to Sweden) is a state secret. Revelation of his existence and of members of the Security Police's involvement in his sex trafficking and drug running organization would cause a major scandal reaching high levels of the government. So in 'playing' against Zala, Salander is playing with a secret that could scorch the careers and lives of everybody associated with Zala's crimes. Any and all of those people would probably burn her right up if they get the chance.
So far, we've spoken rather glibly about Salander's act against her father when she was twelve. But, we have to admit we found it shocking. For some, it will present a big moral quandary. Blomkvist's take on the matter is this:
She, a child all by herself, tried to save her mother's life and defend herself against a psychopath. […] And instead of saying 'well done' and 'good girl' they locked her up in an asylum. (28.110)
Some readers might argue that violence of that sort is never the answer, and that Salander still had other options. Agneta had been beaten by Zala many times before, and hospitalized, and the authorities deferred to the Secret Police and let Zala go free each time. Zala would probably have killed Agneta very soon if Salander hadn't intervened. But, does that make it OK for Salander to firebomb him? Is her penchant for fire proof that she really shouldn't be a free person? Or is it part of what makes her a powerful avenging hero? We'll let you decide.