There has to be something I am not understanding? On the trade screen when it list the luxury or strategic resources, at they the ones we have extra or are they all the resources we have? So if I camped ONE fur, On the trade screen, would that one fur show up?
it's all you have. so if it shows 1 fur and you trade it away, you will be left with no fur. that's probably why you can't get what you want from the AI, it won't trade away resources if it only has one, at least not for a decent deal.