Because the second part of this question is absurd. There is no "process", biochemical or otherwise, that can't be described in terms of information. Information describes the substrate of the "process".
As far as the rest, I never claimed that "processing information" was a sufficient condition for consciousness to emerge. I said that information processing is the thing from which consciousness emerges, and this should not be controversial.
If you understand what "emergence" means (in the context of complexity science) then you'll understand the difference between "conscious" things and calculators.
There's more than one definition of information, and you should be able to tell by context which one is being used.
However, if you want to take this perspective, it just underscores how content-free your claim is. You're then making no claim beyond the basic metaphysical assumption of physicalism, i.e. that consciousness has a physical basis.
It also refutes your own original statement:
> once you accept that our conscious experiences just emerge from information processing in the brain, and that there is nothing stopping such emergent behaviour from happening in computer systems.
You've acknowledged that you don't think calculators are conscious, for example, but they do information processing. This implies that not all information processing systems are capable of generating the proposed emergent behavior of consciousness. That means the you don't, in fact, know that there's "nothing stopping such emergent behavior from happening in computer systems." Without an evidence-backed theory to explain the relevant distinctions between brains and lesser information-processing systems, you simply don't know that.
If you consider yourself a scientist, you should think twice about making claims for which you have neither theory nor evidence.
> I said that information processing is the thing from which consciousness emerges, and this should not be controversial.
And I've pointed out that this is essentially a faith-based position. You have no reason to believe this other than that you assume that's how it must work. You can of course resort to an inductive argument, but those have inherent uncertainty. To claim the kind of certainty you seem to want to, you need to bridge the knowledge gap with faith.
> If you understand what "emergence" means (in the context of complexity science) then you'll understand the difference between "conscious" things and calculators.
If you understand what emergence means, you'll understand that (a) calculators have emergent behavior and (b) you haven't in any way explained, speculated about, or even handwaved a reason that calculators don't have consciousness while brains do.
> For more perspective on what things we know about how the brain works and how it's organized, I recommend reading a functional neuroanatomy textbook.
Why do you think that's relevant? No neuroanatomy textbook provides any explanation of the causes of consciousness. The fact that you're saying this suggest that you don't understand the key problem at all, or why emergence may not be a very convincing solution in this case. While we're recommending things, try Chalmers: https://consc.net/papers/facing.html
Do you think a Raspberry Pi, a 1970s electronic calculator, or a simple analog thermostat is conscious? They all do information processing. If they aren't conscious, what is it about the information processing that brains do that produces consciousness?
This is an obvious false dichotomy:
> There's no magic in the goo. It's all information processing
It doesn't have to be magic. Just to take an example, Penrose and Hameroff proposed that microtubules in neurons are structured in a fractal pattern which would enable quantum processes to occur that (somehow!) explain consciousness. This proposal is little more than a guess, but it's an example of something other than information processing, that's not "magic", that could be a cause for consciousness.
> It's all information processing, and we know this very well.
How do we "know this very well"? The real answer is we certainly don't know that, but perhaps if you try to justify your position, you'll realize that.