When you're hurt, someone else suffers for you.
I am not going to try and make a summary of something that doesn't really have one, it's not really my point anynway. I am not going to go into the so called symbolism of the series, not because I think there's none but because others have done it already and also because I think it's a bit pointless. I won't try to make sense of it because I don't think it's even supposed to make sense. Why you ask? Because I think that, ironically enough, the answer can be found in psychology and the adventures of BRS are a cooping mechanism.
Let me explain why I think that way and then decide for yourself.
Here is what I think happened, starting with the beginning, Mato is a normal student, sadly, what often happens with normal students, they're very weak to stress. So, obviously, when going to a new school where she knows nearly no one and everything is new, Mato is suffering from stress.
And there comes Black Rock Shooter.
In my theory, Black Rock Shooter is Mato's badass persona, the strong one she ultimately wants to be but knows she never will. Kind of her heroine, the one she imagines the adventures of before sleeping, or whenever she has a free moment, at school or wherever.
Everything can be linked to that. Absolutely everything. Remember the evil macarons?
If you think about it, these macarons were used as a weapon in her dream because they have been in reality. But in reality they're harmless, a treat, that's why Mato justify the fact she's been shocked and actually hurt by those and how Kagari gave them by using macarons as a weapon in the awesome realm of BRS awesome adventures.
In that realm she saves Yomi from Kagari and from herself, because I think she feels bad for intruding so much on their lives, she justify her somewhat bad actions by beliving she saves them. And really, didn't Yomi want to be saved? Didn't Kagari want to be saved? Didn't they scream for help?
Thinking about it like that, Mato becomes a heroine and everyone forgets she was nearly a stalker.
That's where Mato's saviour complex really starts to develop, it's exactly as they say, when you're helping people you forget about your own self, technically and even if it will backfire, someone else is suffering at your place.
I know what you're going to ask, what about Saya/Black Gold Saw?
Easy, Saya is a psychologist, Mato did tell her about BRS, then, wouldn't it be logical that she knew what was going on?
Whether or not she realizes it Mato knows that Saya knows, Mato knows what Saya does, she knows how she can control the students by saying exactly what's needed.
They want to be saved from despair. They're desperately looking at the light to be saved, to be helped by a person they're trusting. What does that person do? Make them cry, betray them.
That's where the saviour complex kicks in. What kind of heroine would BRS be if she doesn't help them? How can she save herself if she doesn't help them?
And this, my friends, is what I think is BRS all about, a simple metaphor born from Mato's brain, not necessarily only in her dreams, a transformation of her everyday life in a much more exciting and bearable adventure because, in the end, even if it's only in her imagination, someone suffers at her place.
(See how the rest of the anime will prove me wrong XD)