Polaris, if I'm reading you right you'd say that when presented with a fight, perhaps it's, for instance, a) a lack of mental robustness - to stay calm or b) the ability to endure unpleasant things - in this case fear of being seen as weak, or c) a failure to the meet the challenge of 'peace', that makes a person who goes into a fight a coward.cow·ard/ˈkouərd/
A person who lacks the courage to do or endure dangerous or unpleasant things.
Excessively afraid of danger or pain.
"Cowardice is the perceived failure to demonstrate sufficient mental robustness and courage in the face of a challenge."
I suppose you could swing that definition. I guess it does "work" - the pieces do fit - although it's a bit of a stretch IMO. Really, I'd attribute the symptoms you're suggesting - fear of looking weak - for instance to something more like undue insecurity, or dishonorable insecurity. What you're talking about is trying to maintain appearance despite danger.
Whereas someone who goes into a fight might very well be insecure in the sense of: they may lose something valuable - something of substance, whether tangible or intangible, that is worth risking themselves for, beyond image. In this sense, appearance takes a back seat to substance and value despite danger.
I also think that disco's clarifications are worthwhile.
I don't think these are necessarily contradictory, either.
It's a critical part of the definition to note: cowardice is a perception, and perceptions vary, so there isn't one answer here, but I think it's worthwhile to distinguish motivations.
(And, back to the OP, motivations which also play a role in what is considered "cowardly" in a fight, in my mind.)