If she needs special-ness to do mma, why is she so good at karate? That's unrealistic, it just seems imbalanced. Why did she feel the need to quit her club, what was the real difference? she could have done Kickboxing if she wanted more competition though I doubt that she nationally had it easy.
The main character a bitch but she's not sympathetic. You can have fun at things even when it comes easy.
Also it's a cop out to do it, did they think the audience wouldn't believe the story of a more regular girl getting into martial arts. It's not just here, usually the girls need some convoluted reason for being ultra special in these types of mangas. As oppose to discovery they have talent and learn skill.
also some of it obviously unrealistic, a former pro, less than a year, losing to a girl half his size, that was never a pro... just insanity, and no one is ever more conditioned after retiring than when they are pro. And guess what, even the manga thought so, It back pedals and says it was a stunt.
Still, I guess there aren't many MMA manga yet, especially ones that aren't completely ugly and compared to those, this is more normal, the people are more normal. But like I mentioned, for some reason martial arts girl manga can't be about anyone that isn't already "super" and knowlegeable, and the character acts like a douche even when she doesn't have to. It's not like she's total evil or cartoonish but as a person and character, she's a dick. Now the manga has to start to ignore the way they set her up since it was too unlikable, so they back pedal with her characterization a bit, and randomly added a back story thread apparently because they realize she had flimsy reasons to want to combat and simply saying she enjoyed it wasn't good enough. Still that makes the manga easier to take.
I'm going to add why having such a super special character ruins a realistic story. For one thing, MMA, combat sports in general just don't have a good pay out compare to other sports. Choosing this instead of any other sport that she's so super special in is really ridiculous, not to mention the sciences since she's such a super perfect at everything girl. Second, it sorta spoils the story. A sports story is to find out if a person has what it takes, we're told from the beginning she's special and has what it takes IN EVERYTHING. That she learns so fast she can master anything. MMA isn't special, she just lacks wrestling knowledge. Which she can pick up in an instant since she's so damn specially gifted.
This just probably doesn't match the story, it just has little realism unless her specialness was just physical, in which case, it still spoils the story by telling us that as a fact from the beginning.