@Switch BlaydeThis comment basically addresses the whole thread.
Writing is challenging, and both approaches - "showing" emotions through actions or "telling" them through labels like "angrily" - have particular challenges.
Emotions are driven by thoughts, and for any given situation, different people will have different thoughts and, therefore, different emotions. We have all seen this happen. A group goes through an experience together - a rough day in basic training, listening to an announcement that the company is closing, watching planes crash into the Twin Towers - and yet people experience VERY different emotions because they have VERY different thoughts.
Thus, writers have to get readers inside their characters' heads in order for the reader to truly understand the emotion. Or, they have to do a very good job of building up the character and situation. Why did the captain pound the table? Let me count the ways... uh, possibilities. To get attention? As a calculated maneuver to distract or accomplish some other result? Because he pounds the table a lot and so no one paid much attention and he had to yell? Because he never pounds the table but this time demands it (in his opinion)?
On the other hand, naming the emotion gives clarity, whether in labeling an action as "angrily" or describing a character as being "angry", but it also distances the reader from the story and opens an opportunity for the reader to start to doubt the author. "He is angry," is not a statement of fact, it is a statement of opinion. It can also raise questions as to the insight or reliability of the narrator. (See, for example, "Republicans pounce" as headline material - the use of the term raises issues of reliability and objectivity.)
If an author ever writes that a character experienced an emotion and that emotion doesn't make sense to me given what the story says (or hasn't said) about the character's thoughts, it throws me out of the story almost immediately. This is part of the problem with "insta-love" stories.
So, the best choice - show the emotion or tell the emotion - seems to be just that, an author's choice. But I would suggest that authors have to earn the right to tell, and it's a permission, a trust, that can be easily lost. However, once earned, it can make a story flow more smoothly if emotions can occasionally just be named.
Just thinking with my fingers. Not really arguing or disagreeing with anyone. Thanks for the opportunity, Switch Blayde!