"You can use your sword for plenty of your attacks, and yet still not be a SM if you don't consider yourself one "
You only post a panel showing Zoro saying he has a point. And therefore ignore the context.
Because what King is talking about here in the first place is being a purist. He literally says he doesn't understand why someone would stick to traditional forms and techniques.
So when he says he's not a swordsman, he's not one in a traditional sense.
So in this context, Zoro is saying King never claimed to be a swordsman in that sense.
It still doesn't change the fact that King is "a man who fights with a sword" which means he is a swordsman for a fact.
The Difference and nuance here is that although King is a swordsman by definition, within said definition of being a swordsman, someone's skill level is also usually specified.
Because King treats swordsmanship as more of a hobby that interests him, rather than something to solely dedicate himself to, we can say that King is merely a hobbyist swordsman, in other words: An Amateur Swordsman.
Someone who engages in a pursuit, but doesn't surround their life around it.
That still doesn't change the fact that he is one, even if he is a middling swordsman at best.
And if King hypothetically tried to deny he is a swordsman in this sense, for whatever reason, he would be objectively wrong, in the same way he would be objectively wrong if he called himself white-skinned
You only post a panel showing Zoro saying he has a point. And therefore ignore the context.

Because what King is talking about here in the first place is being a purist. He literally says he doesn't understand why someone would stick to traditional forms and techniques.
So when he says he's not a swordsman, he's not one in a traditional sense.
So in this context, Zoro is saying King never claimed to be a swordsman in that sense.
It still doesn't change the fact that King is "a man who fights with a sword" which means he is a swordsman for a fact.
The Difference and nuance here is that although King is a swordsman by definition, within said definition of being a swordsman, someone's skill level is also usually specified.
Because King treats swordsmanship as more of a hobby that interests him, rather than something to solely dedicate himself to, we can say that King is merely a hobbyist swordsman, in other words: An Amateur Swordsman.
Someone who engages in a pursuit, but doesn't surround their life around it.
That still doesn't change the fact that he is one, even if he is a middling swordsman at best.
And if King hypothetically tried to deny he is a swordsman in this sense, for whatever reason, he would be objectively wrong, in the same way he would be objectively wrong if he called himself white-skinned
Just fighting with a sword doesn't make you a swordsman.
King doesn't identify himself as swordsmen because he doesn't use swordsmanship as his primary fighting style.
He doesn't follow the code and honour of being swordsman (something which zoro highlighted)
And, he doesn't strive to become better at swordsmanship skills
He's basically a hybrid fighter who wields a sword but doesn't live by it.