I know Imoko loves her sister a lot, but holy shit her way to be can lead to absurdly cruel moments like in this chapter, I know well enough how it feels to be in this awkward situation where your image is pretty much crushed in front of everyone, it hurts man.
The worst thing is that imoko is not really a bad person/sister, she loves her sister a lot even if she's a neet (see chapter 18 for one of the most heartwarming examples of this) but the thing is that while imoko is very good at sports and hardworking she's dumb as bricks and can't read social situations at all (she can't read the "why are you following us?" reply in this chapter) so for her telling all those things was no big deal and completely normal.
If she could realize that she's hurting neeko saying all that she would have stopped for sure,but she CAN'T realize it.