So basically she misunderstood the whole situation, cut off all the communion with him without even trying to clarify anything? If not for him trying to understand what the hell has happened and then, once she dropped this whole thing on him, him finding the resolve to take her and clear this stupid misunderstanding, they would have drifted apart entirely
As people above said - quite stupid situation in general and behavior from her in specific, adding this to a fact that she would have given the same answer if had she ever were asked by any of her friends
not trying to make this a "gotcha" or anything, but - have you never exhibited hypocritical behavior?
Just because she might have done the same thing if in his situation doesn't mean that she wouldn't feel dejected, in the actual scenario written into the story. People think one way and then act contrary to that all the time, it's not some fantastical trope solely found in certain genres of manga.
She had two different occasions to overhear him insist she was nothing more than a friend to two different sets of other individuals. The one thing I absolutely think she made a leap at was assuming the cute girl in the second of the two scenarios was his girlfriend, but to me I would imagine a middle school student already in their own head about the truth of the matter would see two separate instances of denial as confirmation that maybe nothing really is going to happen there, after all.
Hell, maybe it's
meant to be seen as "stupid behavior" - we don't actually know what their conversation is comprised of; maybe there's some meta-contextual subtext on the part of the author that's setting up Akira to look like a fool
precisely for "making assumptions" and writing off the potential for a relationship all on her own.
I guess we'll have to wait for the next chapter/set of chapters to know one way or another, but simply calling this "stupid" doesn't negate that it's absolutely something that actually happens, like, all the time.
Given how relatively grounded a lot of this series has been, going this route for the sister who's just falling into the hormonal social mess that is puberty-plus-school seems kind of appropriate, because she's exactly the age group to make this exact sort of error in judgment.