She complimented his outfit and he immediately got depressed and went to change. Even if she didn't hear him that time, it's not the first time she's said something innocuous to positive and had him react negatively. She even questions if he's misunderstanding her because she wears the ring around her neck. But she never shows him the ring.
Now I still see a lot of the trouble as almost entirely shithead brothers fault. But Miyuki has been very dishonest about her feelings. And Sora is still pretty dense for assuming everything she says to him is negative even though she's typically pretty nice to him through her actions and spends a lot of time with him.
I'd argue Sora is less 'dense' than he is 'conditioned'. In large part due to the brother's meddling when Sora and Miyuki were children, telling Sora that "ABC thing" actually meant "XYZ thing" when said by someone from Kyoto--specifically to turn positive or neutral statements into negative or derogatory ones.
From there....MIyuki has the misfortune of
forever having been rather cut off from her emotions. The reason she gets along with Sora as well as she historically has, is because he cut through all of that, and continued pursuing her and trying to talk to her summer after summer.
But even now--even as Miyuki has fallen
hard for Sora, she remains unaware of her brother's meddling from before,
and she's rather obtuse in how she handles herself around Sora in general. As you said - she could clear up
a lot just by showing his ring on her necklace. If nothing else, it'd put to rest all the rumors and badmouthing that goes on about Sora at their school. But she ...just doesn't.
Sora's honestly held himself together rather well all this time, given his constant misinterpretation of Miyuki's words, and the perpetual low-grade harassment and insults he faces from their peers. I think this point, with the added details about Miyuki's grandfather, and the Brother's latest attempt to separate them/get Miyuki to move back to Kyoto, is where the gathering haybale has finally broken the SoraCamel's back.