I'm not sure exactly why compatibilists reject the statement: "I chose fish, and I could not have chosen the meat." It is a pretty straightforward statement of determinism. I think to object to this statement you either don't understand something, or you are rejecting determinism. Since you both raised objections (neither of which got at the heart of the issue), I'm going to try to expand and explain in some detail why I think this is a true statement.

First, I'm not suggesting time travel. Think in terms of a thought experiment that does not need to be possible or practical to make its point.

Second, it was a mistake to use the word "I", especially in quotes because usually what I mean by that is the sense of self of the subject involved, in this case the person ordering fish or meat. I'm not talking about subjective experience here.

And this example, in which I say I chose fish and could not have chosen meat, has everything to do with determinism, nothing to do with indeterminism.

We can take different views of a person. One is we can view them as an actor or agent in a social setting. Another is that we can view them as a subjective self having an internal conscious thought process. Another is to view them as a biological organism, the whole brain/body system. Another is to view them as a dynamical system, a complex machine described by a complex state space.

Depending on our perspective it seems we are likely to reach some different conclusions, or at least emphasize different aspects.

To pin down what the "self" is for a conscious subjective mind is difficult. In fact to pin down anything about subjective experience is difficult. It's easier for us to pin down something unambiguous when viewing a person as an organism or a machine, for the purposes of this thought experiment. The skin is a clear enough boundary, though you could debate about the true boundary of an organism if you went down to the molecular level.

But for this let's say we are talking about the person as an organism bounded by skin, and we are focusing on the nervous system and the brain in particular, and we are going to model it as a deterministic dynamical system.

The thought experiment is, that I have a choice between fish and meat, and I choose fish. The question is, did I have the freedom to choose meat? Of course nothing external prevented me from ordering meat. I had a free coupon for either fish or meat, I like both fish and meat, I'm not a vegetarian, both meals are hygienically prepared in a culinary style I like, I'm hungry, nobody is threatening to harm my family if I choose meat. Lets further stipulate that no sounds, sights, smells, or other sensory input intrude upon my decision. I'm floating in a sensory deprivation tank when I choose my meal.

During some interval of time (not only at a particular instant) when I first am aware of the options, until a second after the choice is verbally announced, this system, my person, will go through a complex series of many state changes in the process of making a choice. We can choose different state variables to analyze this system. We don't need, I assert, to go down to the atomic level, or even the molecular level to capture the states that are relevent to the brain making a choice. The mind seems stable enough that a large variety of molecular configurations can be regarded as equivalent neuronal states. I understand this is the general consensus among neuroscientists, that what really counts is the state of the neurons: their connections, and which ones fire and don't fire, and the number of connections to a neuron which varies the relative strength of a signal. I suspect we could go to even higher levels, if we better understood the functions of various neural connections, and find different sequences of multi-neuron states that are roughly equivalent with respect to this decision process. That is, even with slightly different patterns of neurons firing, a sequence of mental states can occur that are indistinguishable subjectively in the mind of the chooser. So this already indicates the possibility of many thousands of paths through an appropriately defined state space that will deterministically lead this system to making the same decision, and experiencing the same thoughts and feelings. We could add many more paths that involve different thoughts and feelings in the conscious experience of the chooser, yet still deterministically result in the choice of fish. When I say many more such paths, I don't know how to count this, but I think it must be very easily hundreds of millions, which would be a tiny fraction of the possible states of the brain. So lets just say a whole lot of paths. So a given individual can start in many different configurations at many different times, and they will have no choice but to choose the fish. There is no element in this system that is a source of "will" that, once the system begins in a configuration, can change or divert that path onto a different one. This is the nature of determinism. If you disagree with this, you are disagreeing with determinism.

Of course external inputs can change the determined path, but for the moment, I'm discussing the nature of this person as an independent system. I'm talking about the nature of the human mind. Adding external inputs doesn't change the nature of the mind, it just forces it to interact with its environment, and it complicates the number of determining factors in our choices. Adding in external inputs will not add freedom.

I don't know how to count the number of possible states, or exactly quantify the variables for this state space, but given that we have close to a hundred billion neurons and trillions of connections, it would be a very conservative guess to say as a lower bound there exists at least hundreds of millions of initial configurations that lead to the choice of fish, and likewise for meat. I'm not saying these are identical decision processes. They differ in how the decider subjectively experiences them. But they deterministically lead to fish. It's reasonable to speculate that many of these involve -- jumping up to the subjective level -- a conscious experience that feels like it wants to choose meat, and at some point "changes it's mind" to fish before the final choice. This is still just a deterministic march through state space, so even though it feels like there was "free will", the result was inevitable given the initial physical state.

In this deterministic model, when it chooses fish, it could not physically have chosen meat. If you introduce your compatibilist statement "I chose fish, but could have chosen meat had I wanted to", we can say it's true in this model if you started with a configuration that determined a choice of fish, and we acknowledge the hypothetical that if you had started in a different configuration, one that determines a choice of meat and includes the subjective experience of "wanting meat", then you would have chosen meat. I don't see any free will in that though. But it has some coherent meaning.

Popping back up to the subjective level of concepts and language, if you talk about prescriptive ought statements or counterfactuals with "could have done", it seems to me that if you don't link them back to some kind of underlying model that is deterministic rather than linguistic, you are in danger of imagining freedom that isn't really there, that isn't really possible in a deterministic system. One needs to keep in mind that the concepts "ought" and "could" are really just part of the causal chain.

Of course its still practical and reasonable for us to use counterfactuals and prescriptive statements, because we don't need to always refer back to a deterministic model to understand language or behave like natural humans. Part of our subjective decision making process involves imagination and visualization of counterfactuals and prescriptions (among many other things). But if you never refer back to some appropriate deterministic model, it's easy to lose track of the fact that the imagining and wanting and willing and prescribing and deciding parts of our consciousness are just parts of the causal chain, and are not wholly independent units that inject freedom into the process. What resembles freedom at this level is made possible by complexity, by intelligence and plasticity. The will itself is not a source of freedom, but just another part of the causal chain. This semblance of freedom made possible by complexity is what human concepts and language of choice are based upon. It works for us at the conscious conceptual level, and it's the basis for compatibilist arguments about freedom.

But if you want to maintain fidelity to determinism, you need to try to ground "free will" in determinism. From the incompatibilist standpoint a will that is free is nowhere to be found in this physical deterministic system. Compatibilist free will isn't so much a thing as it is a category of concepts that relate to real deterministic human behaviors of choosing, deciding, defending and protecting itself, advancing its interests, learning, wanting, imagining counterfactuals, prescribing desired behaviors, preferring some things to others, fearing suffering, resisting coercion, etc.

So there is some truth on both sides, depending on how you look at things. This is what I mean when I say compatibilism seems concerned with a user perspective, and incompatibilism with a scientist/designer/engineer standpoint. If you want someday to understand the brain well enough to scan it and learn something about what it is thinking, or to interface it to computers or prostheses, or to repair damaged material, you really need to take determinism seriously and use models that explain how it is working at a lower level than subjective concepts.You'll never do these things using compatibilist concepts, and the compatibilist idea of free will isn't relevent or applicable.

At the level of being a human being, and the way we experience things in our subjective conscoius mind, there are a couple of models that work. One is dualism with contra-causal free will. For all intents and purposes, people can pretend these things are true if they ignore lower level deterministic facts about the brain. All of our language works just fine for dualists. They feel like their conscious self creates ideas, effectively out of nothing, by using their own volition, a creative source of ideas and choices that exist only via pure will, an entity that makes decisions as a fully independent agent.

Another model that works at the conceptual/subjective level, without explicit reference to any deterministic models, is compatibilism. Compatibilists can use all the same language that works for dualists: choice, free will, counterfactual possibility, prescriptive statements, and more, but they must be careful about how to interpret these things to exclude dualist meanings. The fortunate thing is that the system of language that works for dualists was evolved in an environment where the humans being referred to, as they always have been, were actually complex deterministic systems. So even though the conceptual basis for some of the words might have been flawed by dualist assumptions, they could largely be preserved with a restricted meaning, because the dualist words were refering to the real behaviors of real people, though presumably for the wrong reasons. For example, from a dualist perspecitive "choice" was unconstrained absolutely because of a kind of special divine freedom. In a physical deterministic system, "choice" is really just the contour of a path through state space that arrives at one result from among a set of options, and can not possibly arrive at any other. The influences which determine that path are very complex though. Many details which are personal to the chooser come into play, such as that person's habits, their preferences, needs, likes, wants, goals, their ability to predict consequences, their values, and so on, all of which are part of the dynamical system. Some of these factors are even visible to the chooser in their conscious mind, so the chooser has the emotionally satisfying experience of feeling like they are making a choice consciously. The chooser can describe their experience of consciously making a choice with lots of the words that fall under the conceptual category of "compatibilist free will". Since there are words that make sense that fit into a category that can be called "free will", people feel this entitles us to say that humans have free will. And exactly these same words can be used by dualists to say we have free will. But the incompatibilist, studying these deterministic systems can not find a thing, a mechanism, a sequence of events that can reasonably be called free will.