Graduation Day 1 
Break Down
Well, so much for 'baby steps'. Faith's murder of the professor was the most shocking thing she's done. However, you really have to delve very deeply into her psyche. By this time, the term 'legally insane' can come into play. We also have to call into play, her childhood. Faith most likely witnessed or was even on the receiving end, of aggressive behavior. A way a child will learn to be aggressive, is from observing adults who are aggressive. It's a huge part of cognitive-social learning. Children who are more aggressive often have parents (in Faith's case 'mom') who use more physical punishment. Sadly, these same parents will also be less accepting and will show less satisfaction with their children's accomplishments. These parents are more likely to punish their children, than reward them. [Eron 80-82] It's more common in poor families due to stress like unemployment and isolation.
If Faith did come from this sort of background, which 
we're fairly sure she did, her behavior is actually predictable! Sadly, psychological case studies prove that Faith would end up in jail. Poor, abused and alone, Faith will do anything for love and attention. Even if it means killing poor Lester Worth. Imagine. . .just for a second, what Faith thinks the Mayor would have done/said if Faith didn't kill him. Faith is getting love and approval from the Mayor. She won't do anything to jeopardize that.
Faith's accidental taking of Alan Finch's life removed her from reality. The shock was too great, hence the denial (a defense mechanism in which we refuse to recognize some anxiety-provoking event or piece of information.) This is what truly infuriates me in Consequences: the bundled hatchet job regarding the 'Scooby Gang's' handling of the whole situation. I (and many others) will gladly tell the world that Faith was in denial. However, Marti Noxon's script calls for Faith to investigate (with Buffy) Finch's death. . .where she admits! she killed him. ". . .he came out of nowhere." It totally screwed up the whole 'denial' track, and ultimately, crippled the episode's credibility.
Coming back to Enemies, Choices, and Graduation Day 1, Faith has herself convinced she's the bad guy. That she can do no right and, thanks to urging along by the parental figure she's been aching for since Faith, Hope and Trick, she settles into the role. Faith has few qualms about unleashing her Slayer side for negative purposes as she knows she'll get praise and approval for it. The added bonus for her, is that she's free of Buffy and the moral high ground that comes with being with Buffy.
Keeping us intrigued, was Faith's stroll down memory lane. Obviously a memory that just 'popped' into her head after the Mayor calling her "Little firecracker." She tells us that her mom used to call her that. . .but then she trails off. Again, only saying what she wants to say, I believe that the ending of that memory is not pleasant. Perhaps along the lines of her mom calling her that before she was on the receiving end of her mother's abuse. It's a memory that is bittersweet. Note that Faith becomes aggressive immediately after—asking if she'll get to fight at the accession.
Faith's esteem, despite the praise the Mayor heaps upon her, is still quite low. Sure, she's had moments where she felt great, but overall, she doubts herself. She's frightened of letting the Mayor down. Indeed, in the scene in the apartment, it's the last thing Faith says. Again, as throughout the season, Faith will only say what she wants. She always edits her thoughts. She never speaks extemporaneously. There is a whole other side to Faith that she never lets anyone see. But, if we dig deep enough, by observing her actions, facial expressions and what's left unsaid—we can come up with a rough guide to her. At the end of the day, Faith is the young teen that was quivering in a corner while Buffy tried to kill 'Kakistos'. She hasn't really come any further. In fact, she's been let down time and again. She expects to be let down. She expects everything to go wrong for her.
In this episode, Faith seems to welcome Buffy's 'visit'. (Also, by having Angel on death's doorstep, it assured a visit from 'B'.) Frankly, I believe Faith knew Buffy would win. Although there seems to be a genuine part of Faith that believes she can beat Buffy—in her heart she knows she probably won't. It begs the question that 'Did Faith already see herself the way she does
in Who Are You' There (for me) is a huge question mark over Faith's bravado—as there has been throughout the season. We've seen it from Faith, Hope & Trick onwards. But I still believe, despite her fighting skills, that Faith is always frightened that she's not good enough. Both Slayers had seen enough of the other fighting to know what to expect. Faith, perhaps believes that her wild abandon would win out over Buffy's control. However, she didn't seem too shocked at losing. Indeed—just a second before Buffy knifes her, Faith tells Buffy "I'm gonna miss this." It wasn't said by someone who felt they'd win. It was almost sad. I've got to say too, that Buffy didn't seem to be delighted at what she'd done. She took no pleasure in it.
A lovely link with Enemies has Buffy telling Faith to "Stick around." It's Buffy's way of letting Faith know that she's as ready to kill as Faith was in Enemies. (Although-I'll never believe Faith would've killed Buffy in Enemies or any episode. I believe Faith enjoys the sparring, but not to the point of killing). Even though it seems Faith has lost the fight, she's still got a card up her sleeve. Upon seeing the truck, Faith believes she can escape via it (although-falling backward?). Whether she intended to die or not, Faith did tell Buffy she wouldn't ". . .help your boy. . .". And she made good on that. She probably thought she'd die on impact. Time and again, I believe Faith believes that no one would miss her if she died. Almost, like she'd be doing the world a favor. And that's the saddest part of all. It's why we love her so much! We want to rescue her from herself. That's Faith's appeal.