The conventional understanding of existence, where everything is made of matter and consciousness is a product of matter, is completely backward and could not be more wrong. I'm going to point out all the many plotholes in this understanding of the world and show that consciousness must exist independently from matter, not vice versa.
Argument One: Free Will
The existence of free will is incompatible with the idea of a physical mind. In a physical system, every event is caused by the previous event, every chemical reaction by the previous reaction. While some modern scientists might argue that physical reality is actually probabilistic rather than deterministic, that doesn't help - randomness isn't any closer to free will than determinism. But the whole idea of free will is that nothing causes it. It could have been different without any of its precendents being different, yet the person has control of it. There's clearly an irreducible concept of "choice" here that cannot be a product of determined causation and randomness.
Now you might get to messing with the concept of personal identity to get around this. You might argue that "I" am my brain, and so whatever "decision" my brain makes is the "choice" "I" made with my "free" will. But then you'll notice you've redefined free will so that the definition is still met if external factors - the genes I was born with and my experiences - determine my actions, and therefore I would still have free will if my brain were controlled by a neurologist. That's not called free will!
Therefore the only way to really have free will is if your decisions are actually coming from some protected space outside of physical reality.
This is what I call a "soul", or more accurately, a person (since it is a person's behavior that defines "who" they are). A person can control their body through their brain, and can perceive the world through it, but the person themselves exists outside of their brain and is not controlled by it.
Argument Two: Epistemics
The key realization here is that we have never seen anything but consciousness. Everything we believe in we only found out about through conscious experiences. We have not, and cannot, experience any facet of any physical object other than the perception of it. Therefore we have no basis for believing that they exist independently of conscious experience. And by "no basis", I don't just mean there's an unfulfilled burden of proof; I mean we can't believe in such a thing because we don't know what it means to exist without consciousness. The only definition of existence we have is perception. Believing that the physical world exists independent of consciousness is saying, "there is some kind of existence which can never be demonstrated and can never be understood." That's actually the least scientific thing I've ever heard.
Argument Three: Intentionality
If my consciousness is a product of specific patterns of matter, then you must argue that those patterns of matter couldn't exist without being conscious (because if they could then there would be two physically identical systems with a mental difference and therefore minds couldn't be a product of physical reality). But is it possible to hold that position?
All of science is about studying how matter interacts. There's nothing else to study in science because that's all we can observe. And therefore it's impossible to say that there's something to matter besides how it interacts.
So materialism holds that it is impossible to have a system that behaves in a certain way without consciousness. Materialism requires you to think that patterns of causal interactions between matter are what define consciousness, which is clear nonsense. At that point you might as well say consciousness doesn't exist. It's also obviously wrong for another reason because the concept of consciousness is coherent without knowing the science behind brains.
Argument Four: Universal Morality
If everything about our consciousness is a product of our brains, and our brains are a product of evolution, then our sense of morality is also just a product of evolution. And that means that by our own ideas of morality we can't hold our ideas of morality to be morally legitimate, because our source for them is just an arbitrary product of where and how our species evolved. There could be alien races that evolved to have a different idea of moral behavior and according to materialism, there's no way to argue that ours is better than theirs if they say murder is okay.
Therefore, our conscience must exist in an immaterial soul, not as a facet of the brain.
And if you're going to try to argue morality is based on logic and doesn't need a conscience, then you need to think that through more, but even besides that this same argument collapses the validity of our reasoning.
Argument Five: Reliable Reasoning
You have to believe in the soul to believe that your own reasoning is valid. If your brain, and therefore your reasoning, is just a product of evolution, then there's no reason your reasoning would be valid. Natural selection would have given you a mind tuned for survival, and since philosophy has basically no bearing on survival, it wouldn't have given you the ability to understand metaphysics.
So materialism makes it at best a shaky, unprovable assumption that it's even possible for us to reason about metaphysics validly except by a fluke.
So what's the truth?
The universe can be explained as an algorithm by which souls are able to influence each others' experiences, but it cannot be meaningfully understood as something that exists in its own right. Let me answer another objection here: how do new souls get added? Clearly human procreation creates new souls if what I'm saying is true, and therefore physical things can have direct power over souls, right? No; it gives souls a causal link with the universe that didn't have one before, which is only "creating a soul" insofar as you understand that existence is defined by consciousness and thus that "creating" a soul doesn't actually mean anything besides giving it its first experience. Souls having power over other souls' causal links with the universe can be understood as an extension of souls having casual links with the universe.
Once you understand this, you can already see it ceasing to make sense to say that any part of the mind besides perception can be directly affected by physical things. If such a thing is possible then why does perception exist? Why doesn't our eye seeing a tree in front of us just directly cause us to believe that the tree is there? I know this doesn't really prove that such a causal influence can't exist; but it constitutes a reason to believe what I'm saying unless you can prove it wrong.
The Problem of Sleep?
Objections related to sleep, dreams and death are handled here.