It's not the degree of prediction, it's the very basis of the hypothesis. If warming of the same magnitude happened several centuries ago we can argue that it is not driven by human activity, that CO2 is the consequence and the cause of warming and that proposed measures are a waste of time.
Actually, no. If warming was happening several centuries ago it could absolutely be the product of human activity, and even if it wasn't it could still be caused by natural sources of carbon entering the atmosphere, and further, the remedy--removing carbon from the atmosphere--would still remain the same. So all you've got is sophistry and pedantic, nerdy objections to modelling, and since I work in a modelling heavy field I can assure you, that's all myopic little bug men are capable of doing: arguing about details of a model when the fundamental truths are as plain as day.
You have two "could" and one questionable "would". Doesn't seem like a solid basis for a model to me. I work in a modeling heavy field too - diagnostic and treatment algorithms in anaesthesiology are based on models of physics, physiology and pharmacology. Moreover, I used to design trading programs in my derivatives trading days. Mind you, derivatives markets are highly volatile and unpredictable, however, if I designed trading with results like what they have in climate we would abandon this approach very quickly. That's the difference between "climate science" where you can either make unverifiable predictions (one hundred years from now, for example) or get away with meek explanations if your predictions are completely off and still keep credibility, while in financial markets the only credible proof is your trading account. Similarly, if my patients take longer to wake up, mortality is higher than the average or if every one is vomiting - my theories will not be taken seriously.
What you call pedantic and nerdy is actually essential for verification of modeling. Look at the diagram I posted earlier: ALL of the models are based on CO2-temperature theory, NONE of them have predicted what was actually observed, the AVERAGE of all of these models is off, and MOST of the models are off by a large degree. That's sufficient reason for someone with basic understanding of scientific methodology to question the theory, the fundamental truth as is plain as day to you. What would you say of an antibiotic that cures pneumonia in zero percent of patients? Or investment methodology that never produces profits?