a) he mocks her thus creating mental challenges and obstacles for her
b) he's regardless of his gender a love threat to the main couple
Yes, but how are those "mental challenges" related to Seol-a's goals in the story as the protagonist? Being an asshole to someone and annoying them doesn't make you an antagonist. That was naturally a part of his personality, and Seol-a knows this. We all know that Ji-hwan cares a lot about Seol-a. He would never hurt her intentionally; like Seol-a has said herself, Ji-hwan is like a brother to her. Being a part of a love triangle doesn't make a character an antagonist either.
When Ji-hwan intervened with his confession, there was no "main couple" to become a threat to. At that point in time (ch.25), neither No-rae nor Seol-a had acknowledged their feelings for each other. No-rae's reason for rejecting Ji-hwan wasn't because she liked Seol-a either, it was because she didn't feel ready for a relationship.
reread the chapters ~10-15 or so to recall how Seol-a caught herself disturbed by Ji-hwan x No-rae
She certainly was disturbed, but not because of romantic concerns. She only realized her feelings for No-rae very recently. According to chapters 10-15, Seol-a was disturbed due to the fact that she was suspicious of whether No-rae was using her to get closer to Ji-hwan or not. She wasn't jealous of No-rae's relationship with Ji-hwan.
everything directly or indirectly pointed to Ji-hwan as the source of her irritation
Once again, irritation =/= actual mental distress. The idea that No-rae could be using Seol-a to get closer to Ji-hwan caused Seol-a much more grief than Ji-hwan himself ever did.
And that is precisely what made Ji-hwan and Kyung-woo antagonists. Villains? No. Archenemies. No. Antagonists? Yes.
Archenemy and villain essentially mean the same thing as antagonist. However the term "foil" is not synonymous with antagonist. Ji-hwan wasn't an antagonist for being a foil, or for confessing to No-rae. You could argue that Kyung-woo was an antagonist during his arc. Kyung-woo was romantically pursuing Seol-a, even going as far as to use dirty methods like getting her completely plastered, but No-rae confronted and stopped him. Throughout his arc (chapters in the early 30's or so), No-rae was aware of her feelings for Seol-a (ch. 27), and so Kyung-woo's actions clearly opposed her goals. He presented a challenge that No-rae felt that she had to overcome. If you compare and contrast Kyung-woo and Ji-hwan's situations, you'll see why it makes sense to say that Kyung-woo is an example of an antagonist, but Ji-hwan is not.
manipulative personality and him being the "obstacles" origin for Seol-a when it comes to No-rae
I honestly don't know where you got the idea that he has some sort of evil, manipulative personality. I can't think of any examples where he tried to use someone to gain something for himself. Like I've said before, when he confessed to No-rae, Seol-a wasn't aware of her feelings, and so she should not have considered him an obstacle. She was still distressed after hearing about his confession due to her underlying feelings, but her situation with Ji-hwan was nothing like No-rae's confrontation with Kyung-woo.
Compare Seol-a's reaction to Ji-hwan's confession to her reaction when she believes that her brother supposedly gets a glimpse of "No-rae" on her phone. Now that she's acknowledged her feelings, her reactions towards others getting close to No-rae are clearly different.