They confuse and corrupt. They undermine authority and erode professionalism. They are the mortal enemy of rational decision making. Emotions are not for professional warfighters. Emotions are for teenage girls.
Your watch team will follow your lead. If you react emotionally to a tense situation, your operators will swing in that direction, and professionalism will crumble. Formality and efficient communication will fall apart at the worst possible time. If you are even-tempered and calculating, on the other hand, your example will be followed, and this may be just what the team needs to return to thinking clearly and performing as trained. In a tense, frustrating or chaotic situation, you should be the calmest person in the room.
But what about situations where anger is necessary to establish discipline? Our old pal Cicero addressed this a while back:
Sometimes it happens that it is necessary to reprove someone. In that case we may perhaps need to use a more rhetorical tone of voice, or sharper and serious language, and even to behave so that we seem to be acting in anger. However, we should have recourse to this sort of rebuke in the way we do surgery and cautery: rarely and unwillingly.
I’d add that deliberately suspending emotional control (or pretending to) should only be attempted after very careful consideration; in other words, Never lose your temper without a plan. That said, I really don’t think you can go wrong with the simpler version, Never lose your temper. A warship at sea is neither boot camp nor is it a high school locker room. Making a scene is distracting, grotesquely informal, and almost never appropriate in the vicinity of people operating dangerous machines (like, you know, warships). It is entirely possible to communicate even extreme dissatisfaction without losing control, and a leader who consistently displays self control will command far more respect than a leader who displays a lack of it.
Stoics believe that every degree of emotionality is a step away from self control, and as such is inherently counterproductive. The ideal amount of emotion (when acting in a professional capacity) is zero. I’ll qualify this by narrowing “acting in a professional capacity” down to when actually on watch or otherwise making decisions which affect others– indeed, everyone needs the occasional break to step away from their professional role and be a human. That said, I’ve found that as one progresses in their career, opportunities to “step away from the professional role” become fewer and less frequent– particularly while at sea.