A quick check seems to indicate that there is some question as to whether anger is a primary or secondary emotion. Here is an article which would show anger as a component of one of the six primary emotions.Here (from the same article) is a chart showing the origins of said emotions.
From this article I get the following definitions:
What Are Primary Emotions?
Primary emotions are the immediate emotions felt in response to any given situation. They are felt first, and reflect your true feelings regarding the situation. They are unthinking, instinctive responses. An obvious example is feeling fear when confronted by something intimidating. These emotions often last for only a few moments.
What are Secondary Emotions?
Secondary emotions, as their name suggests, follow after primary emotions. They can sometimes confuse your perception of how you truly feel about a situation. This is because initial emotions may only be experienced for a split second, after which they are replaced with secondary emotions that linger. Secondary emotions are often more complex, and they may be mixed (for example, you may be happy your daughter has got married, and yet you are sad that she has finally grown up and “flown the nest”). These emotions tend to be less primal, and often involve intellect and reasoning.
Is anger an immediate unthinking emotional response (to me it certainly could be) or is it less primal, more thoughtful reaction and the result of some other emotion (again, could be)?
I think I can see why there is a debate.