Labels are boxes a person can reside in or be put in. Which makes them equally good and bad. Like you just did now, you put her in that box (lesbian or bi) and you might be right, and I'm quite confident, you did it out of care and maybe understanding, but it's not your place, to put her there - that's where insisting on labels is wrong. If she wants a label, let her take one herself. If she never wants a label, that's fine too.
Openness and sharing knowledge about our labels and working towards tolerant environments is always something I'd support though <3
This is a manga character, she won't read what I wrote. If it were a real person, I wouldn't insist on giving them any labels, but manga stories are usually direct in their messaging and this one's quite obvious, even Tengoku thought "I understand her, because I like *you*"
.
"Why do you insist on labels? Trans, bisexual, lesbian, asexual, we're all just human!"
This is why.
This poor woman was clearly in love with her best friend. If she grew up in a more tolerant environment, knowing those labels and the people behind them, she might've known she was a lesbian (or bi) way earlier. Labels are important and we all have them, whether we realise it or not.