it's no surprise Akira struggles with getting close to people when her first instinct to being confided in is to either get knee-jerk judgmental or privately consider you weak.
i also think she's misunderstanding the situation... Rin wants to be teaching the "non-school stuff." Akira can frame it as helping Rin out of an ethically weird situation but her solution is just an attempt to displace the mayuki/rin relationship and mitigate her own jealousy. Neither of the other two girls fit the boxes Akira has placed them in. She seems to think they're both clueless, vulnerable, and unable to make sensible choices on their own, so she needs to step in as a voice of reason, when her own actions are also teenager-typical levels of irrational.
Interested to see if/how her attitude changes. my guess is that mayuki will surprise her.