@SemperSolus To add on to what
@darekpawlo said,
Togawa isn't just quitting her job, she's pursuing her passion. I imagine many people don't really understand why some people decide to try improve themselves alone.
"Why does she have to stop seeing him to be writer?" I probably can't explain in a way that's satisfying. People that do this usually do so for a few reasons. In some cases, especially for introverted people or artistic types, seriously trying to get better at the thing you want to do means spending every waking moment on it, sometimes at the expense of not seeing other people . She's shown in the chapter to have saved up a lot of money beforehand, meaning the thought of quitting her job to be a writer has been in her head for a while now. In addition, Eastern Cultures in general (from my pure speculation) have a history of romanticizing the "solo journey to improve one's self." Depending on the person, it's much more emotionally satisfying to improve by one's own effort instead of relying on those close to you. It's not just about being better, it's also about hoping to make the people you look up to proud. Togawa has shown in the past that she has some self-esteem issues, so she doesn't even have the confidence to face Mamoru herself, but still wants to tell him that she'll reach his level someday, which makes Mamoru running after her very "emotional" and super manga-like.
As for elevation, Mamoru telling Togawa that they'll meet somewhere "higher," has a dual meaning. One is Mamoru giving a vote of confidence in her, believing she will definitely improve, but also lets her know that Mamoru thinks that Togawa has the potential to surpass him as he is now, but he won't stop growing either. It's more than just saying "you can do it" and is also super manga-esque.
So, It's not so much emotional manipulation, but likely a combo of differing values and manga tropes that only work if you can get behind the values in the first place.
Admittedly, quitting your job to become a writer is risky no matter what culture you're from.