This is the most important principle of Protagonist metaphysics. In short, everything about our consciousness is actually in our souls and not in our brains. Your thoughts, your memories, your emotions, none of them have anything to do with your brain and things in your brain can't directly alter them. The only thing the brain does is allow us to control our bodies and forward perceptions from sensory organs to our minds. There are several reasons why you should believe me.
The first is that the existence of free will is irreconcilable with the idea of a physical mind. In a physical system like your brain, every event is caused by the previous event, every chemical reaction by the previous reaction. But that's not how free will works. If you have free will, your previous thought does not cause your next thought. Nothing does - you choose it. Therefore your free will has to be coming from somewhere other than your brain. Additionally, it should be pretty undeniable that the mental faculties I listed above couldn't possibly exist without each other, so that means if one of them is only explicable as an immaterial entity separate from your brain then the others must be in your soul too and not in your brain.
The second reason you should believe me is what I call noncontingent morality. So here are a couple of premises you believe if you are a conscientous person: 1) Conscience is an infallible source of moral teaching; 2) Morality is the same for everyone. Now, if your conscience is in your brain, then its teaching could have been different because your brain could have been different. That means there could be a sapient being whose correct morality is different from ours - a metaphysical impossibility.
Third, for the same reason you should believe that your own reasoning and introspection is reliable. If your thoughts can be directly altered from your brain, then you can't know that an evil scientist hasn't implanted you with a chip that prevents you from ever reasoning validly and from remembering the event. If you've read the lesson on the Principle of Contingent Uncertainty, you already know that you can't technically 'prove' anything about the world around you, although there are still reasons to act like it's real. Well saying that your brain houses or at least controls your thoughts is basically making the same thing true about your mind.
The fourth reason you should believe me, is because you already do and you can't help it. I have some thoughts files on my computer where I was trying to figure out what primary emotions can exist in the person's mind and exactly what causes each of them. I decided that we feel joy when our desires are fulfilled, sorrow when our aversions are fulfilled, fear when our aversions are about to be fulfilled, etc. And that all makes sense, right? But if we accept that our emotions can be directly altered from the brain then all of that becomes meaningless because what really fuels those emotions is just some chemical reaction, not anything that philosophy can figure out except by coincidence. Is that something you believe? That what fuels emotions is a matter of science and not philosophy?
In fact, I go so far as to say that these immaterial souls we have are the only things that exist - the physical universe does not except insofar as sentient minds perceive it. I can't really explain it, but in my teenage years I just sort of had this epiphany while sitting alone on a pier at night, and ever since then I haven't been able to see it as not self-evident that if a physical object can never be perceived, it by definition doesn't exist. (The reason souls aren't subject to this is because we perceive ourselves through introspecton.)