I'm sure many will disagree with me (and that's fine) but Barbarian Rage does not have to equal "anger" it can be primal will to survive. Conan often, perhaps even always, fights with ferocity that a warrior raised in a civilized society just can't equal.
Take for example, Beyond the Black River where it states the difference between Conan and Bathus is that Conan was raised in a society as savage as the Pict's and that is not something that a Civilized man like Balthus could ever "learn" no matter how many battles he wins. It's innate.
I quote from that story: “Barbarism is the natural state of mankind… Civilization is unnatural. It is a whim of circumstance. And barbarism must always ultimately triumph.”