Downplayed: Jim will not fight against any women who are gentle, lady-like and do not like to fight in the first place. Female enemies and violent tsunderes are considered Acceptable Targets, and Jim would be willing to smash their faces off.
Veridian convinces Jim on how thinking that indirect attacks being okay is a very stupid idea and Jim reluctantly agrees.
While Jim did mention he had other reasons why he wouldn't want to fight Viridian he eventually admitted that this trope is one of them.
"I'm so not gonna fight you even though I know you have no mercy for any one and wouldn't hesitate to kill me on the drop of a hat. No, ma'am, I'm not gonna defend myself because I'd rather be dead than be known as woman-beater."
Jim refuses to fight Veridian because she's a girl. However, he later discovers that 'she' is actually an alien who has taken the form of a human female. Just when he is about to attack the shapeshifter, she reveals her true form to be a Green-Skinned Space Babe.
With Loophole Abuse, Jim uses his machine gun to shoot all girls down. On one hand, he isn't physically hitting them, but on the other hand, well...
The writers don't show Jim and Veridian fighting because their afraid of offending viewers who would object.
Or the writers have little to no knowledge of men attacking women and being seen as a good thing while they are a little too used to all the times when it is very much a Kick the Dog moment from Would Hit a Girl trope using villains.
Lampshaded: Jim is getting stomped. In the middle of it all, he says "You bitch...you're cheating by beating on me while female!"
Invoked: "People think Jim is too tough and heartless. Let's show that he's actually nice by making him against hitting girls."
Defied: Jim and Veridian get into a fight without any ramifications about breaking any moral code.
Discussed: "It's not that Jim couldn't take Veridian in a fistfight; it's that his inconvenient chivalry would kick in."
"I wonder why some guys have no problem fighting a man, but wouldn't think of hurting a woman."
So he doesn't want to fight ladies huh? Let me guess is he one of those "will not fight back against a woman at all" guy? Or is he a "will not punch a lady in the face" kind of guy?
Jim's refusal to fight Veridian is seen as an insult by her because that means he views her as weaker than he. She responds by handing him his ass
Veridian tries to convince Jim to have a friendly fight with her to beat the sexism out of him. She is often seen egging him on and generally being aggressive toward him. She may or may not praise him for finally losing the sexist attitude if he caves and hits her.
The females abuse this and bully a guy since they know he can't hit them.
Jim's refusal to harm a female makes him a greater threat to his True Companions than Veridian.
But before she can do so, Marci gives her an epic beatdown, and saves Jim in the process.
Jim's a Technical Pacifist. His fight style revolves around blocking attacks and jabbing nerve clusters to cause paralysis.
Veridian kicks at Jim. He catches her foot and uses it to steer her around like they're playing "wheelbarrow".
Veridian is a masochist, who wants Jim to hit her.
Played For Drama:
The hero has to beat a woman to save his friends. Can he?
The hero´s enemy is a sadistic Dark Action Girl, he refuses to hit her, she completely beat the shit out of him with a Slasher Smile, insulting and toying with him and leaving the guy crippled at the end, with several bones of his body broken. He realizes that the injuries in the body are so severe that he won´t be able to fight anymore, so he will be an invalid the rest of his life.