first off, why does glasses girl care for short hair girl? (and the other way around too)
Katagiri is extremely passionate about music, moreso than anyone else she knows; it's stated she's the only person who practiced in the mornings her entire time in high school, until Aikawa transfers. Aikawa is the first person she's ever met who cares about her passion as much as she does. Furthermore, though, Aikawa comes at it from a completely different direction. While Katagiri wanted to individually stand out as the first trumpet, Aikawa wants the orchestra as a whole to sound as good as possible -- her favorite part, recall, is when the first and second trumpets overlap. This idea deeply moved Katagiri. It's hardly outlandish to me that feelings would develop from these factors, it's honestly a much better reason than we see in most romance manga, where it tends to just be "they're hot" and/or "they're nice."
As for Aikawa's feelings, we still haven't gotten much from her PoV so it's hard to say for sure, but playing the same instrument together with someone and spending time in the mornings practicing with them is more than enough basis for friendship at least.
the world feels empty, like there's no other people appart from the 2 main girls, and there's nothing else than playing in that band they are.
It's been four relatively short chapters and we've already seen the guy, the band's conductor, Katagiri's kouhai who might have feelings for her, and the blonde glasses girl who seems to be the club's president or something.
The band is pretty much all Katagiri is but that's also the point of her character, what with how uptight and serious she is. On the other hand, the band is very much not all that Aikawa is, and that's precisely the point of conflict between them.
why is she with that guy, be it just to fool around or whatever, is weird too; even if you say there's no feelings involved at all, there's still gotta be something funny or thrilling about it for them; it looks like their lips are just touching and that's all lol
I don't see how it's weird. She's with him because it's fun for her. It's implied there are other possible reasons but like, what else do you need lol.
why is she being harassed (verbally) by the director (or was harassed, i don't know if that's supossed to be a flashback or not), wasn't she the first trumpet, like the best and chosen by the director himself? he just decided to hate her on a whim?
First, it was a flashback, you can tell because of the black border and also because it's a different conductor from the one in the present day (easy to tell because the present-day conductor is a woman). Second, I actually think this part is the weakest of the manga so far because what the guy is saying doesn't make much sense, but it appears that he's criticizing the tone/mood of her trumpet playing, saying that it's not appropriate for the segment that she really wants to play. The idea seems to be that, while Aikawa does love music, she feels stifled by all the restrictions and expectations placed upon her by others. I assume it'll be explored more in future chapters.
why is she first trumpet too, we didn't even see why she won and glasses lost
Because she's a better trumpet player. What other reason could there possibly be?
I think @Kirin-kun saying you just want to be spoonfed was an unnecessary insult, but all the questions you've asked do have relatively straightforward answers that you can figure out by reading the manga and drawing natural conclusions. My honest suggestion is that, if you're confused about something, spend some time thinking about what the reasons might be, don't just assume it's a problem with the manga.
If I have to read all that to get what's going on with the manga and actually get interested in it, then the manga is not doing right
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