I think you've seriously misinterpreted this scene. The teacher saying, "I'm not abandoning you," is not a highlight, but a foil to contrast Saki's true inner state. Saki is sad because her love is unreciprocated and her crush has been 'taken' by somebody else. The piano teacher is oblivious to this and assumes that Saki is sad because she feels abandoned, even though this isn't the case. The line is highlighting Saki's masking and the invisibility of her struggles, which is truly what has been a throughline throughout the story.
Saki feeling sad that she's losing her crush IS Saki feeling abandoned. Her teacher doesn't know Saki's feelings, which means that she isn't able to understand that replacing herself with a new piano teacher doesn't actually make it so that Saki doesn't feel abandoned by her, because her role as Saki's teacher isn't why she was important to Saki. She suddenly left a hole in Saki's life that a new teacher simply doesn't fill.
Also, it's important to realise that Saki's struggles are only semi-invisible. Yes, she keeps things inside, but one of the throughlines of the story is actually the extent to which other people DO notice different parts of her (and Kanon's) struggles (but never the whole struggle) and reach out to help them confront them. Akira talking about her own experience as a queer adolescent is a great example of this.
That's relevant to the chapter where Saki acknowledges that her talking to other people hasn't fixed her issues and refers to herself as her enemy--she's trapped by her own presumptions about the people and the world around her. Saki's presumption that Kanon is into older men in Chapter 8, which causes Kanon to get mad at her, is an early example of how Saki's tendancy to jump to, and act upon, negative presumptions is holding her back.