A strawman of the argument I then proceeded to make, and which I would think any reasonable determinist/compatibilist would make.
This sounds more like scientism than what I would understand to be a correct application of science. The very fact that you portray the opponent as proposing seemingly immutable laws, when in fact natural laws are nothing more than our best attempt at formulating successful models for empirical prediction, seems to indicate a less than rigorous thought process behind the claim.
Well, the simple answer is that thinking one is in a deterministic world typically doesn't make one very happy. Not to say that it can't, but the amount of protestation would seem to indicate to me that it is not one of the more cherished ideas to have been proposed by philosophic thought. On a more serious note, the difference, if I am able to point to one, is that freewill is based on our folk psychological self-assessment with no controlled test. On the other hand, denying freewill is to do nothing more than apply inductive reasoning, on the basis that we observe what seems to be determinacy and indeterminacy, but nothing between these two, and in fact have a difficult time formulating something between these two. If this applies to nearly everything around us, and that the violation of that pattern is us, and that only based on our self-assessment, than it seems at least plausible to doubt that self assessment. As I said earlier, it is not a necessary conclusion, but a conditional one, based on observation of the world around us. It could very well be wrong, and anyone who proposes it ought to know that such a conclusion cannot be "immutable" or inevitable. Back to the difference though. The human brain is indeed the source of the freewill proposal, but I do not think it is the sole source of a deterministic proposal, since that would require it to generate all of its own sense data. This is not impossible, but it does seem unlikely, and if such an idea is advocated, then there is no point in arguing just about anything because there is nothing to know and we are all trapped (if there even is a we, since such a person is reduced to solipsism) in the world of our own mind.
No, I don't think the loop, if there is one, works in quite that way. Being conditioned for causality is not the apparatus that makes us think we are free. It is merely a tool for dealing with the world, an attempt, if you like, to get a handle on the world by framing the discussion in terms that demand predictive models. As an evolutionary trait, I think it is probably one of the most successful ones developed by biological life on Earth. It doesn't demand freewill however, except that it is built around efficient success, and so does not demand greater accuracy or sophistication in the explanations it develops than would give it good returns on its intellectual investment. If an additional 2% predictive success requires doubling the mental effort to achieve, then such a model would not be inclined towards it. Folk psychology is just that sort of rough, yet efficient and successful, estimate of behavior. And given the lack of other models for most of human history and the relative success of this explanation, it makes sense that it would almost unhesitatingly be applied to oneself as well. As for how the brain can understand these things, we can understand all sorts of things that were previously taken to be de re, but are now understood to hide a complex confluence of multiple influencing factors. Consider, even if we find our brains incapable of picturing four dimensional space, we are still capable of understanding things about it, mathematical and conceptual models that give us at least some idea of what it might be like.
Naive realism is an eminently useful way of looking at things. It is efficient in both its communication and calculations regarding the world around us, and where precision is not as important (as when I need you to hand me an eraser), it works better than most any other model I can think of. And I agree that no one should be saying, or even suggesting, that determinism is a slam-dunk. It seems the clearer choice to me, but this is based on contingent knowledge of the world and is falsifiable at any time.
As to how one can hold it on a practical level, I can live with it realistically the same way that I live with naive realism. I am quite happy to operate, both mentally and linguistically, in a naive realist framework. It is the way my brain, and I assume most other people's brains, are inclined to see the world, and unless there is a pressing reason to drop it in favor of a more precise model, I see no reason why I should tax myself to perceive the world in this way. It is simply the easiest, most efficient, and simplest way to go about my business. My view of folk psychology and self-determinacy is much the same. Given how much of our society and personal interactions are based on it, a compelling reason for greater precision would have to be present for me to consider a different model. Without that, I have no reason, no "motivation" (got to love the irony there, eh?) for pressing the matter. The contradiction you noted is real, but only because the language being used is built around this model. It is the same sort of contradiction you see when someone says, "Unicorns do not exist". How can you say that sentence means anything if there is nothing being referred to (and there is nothing if Unicorns do not exist). It is a grammatical contradiction, not a logical one, and is demonstrated to be so once we see that a different sort of grammar can be used to express the same thing, only this time without the ontological commitment, "It is not the case that there is something that fits the description entailed by "Unicorns". But do you see also that the first is much more efficient, and is perfectly adequate so long as there is no confusion as to the nature of the expressions grammatical object.
I'm not sure what you mean by science behind freewill.