I've seen this across several different anime, although I don't have a specific example right now.
Typically the attack will be a barrage of projectiles and the defending character (e.g. the main protagonist) hasn't landed a hit yet or otherwise hasn't revealed how much of a threat he is yet. I understand the translated term "running away" is meant as a jeer against the protagonist. However, the protagonist is still engaged in active combat, and I would think "running away" means attempting to disengage. In this case the taunt has faulty logic. I understand taunting does not need logic, it is meant to strike a nerve and make the target more predictable.
Is it that tactical evasive maneuvers are considered cowardly and are disallowed in Bushido? I'm basing this guess off of an example in One Piece; When Zoro initially duels Hawkeye, gets struck and is about to lose, Zoro asserts that taking a step backward is equivalent to breaking his oaths and forfeiting his ambitions. This might not be the best example though since the characters, during combat, including Zoro, have no qualms against preserving their own life by dodging attacks, which is the context of this "running away" taunt.