Shiemi is socially challenged and Rin didn't understand her.
. . .
shiemi said she nerver had a friend before.
izumo is her first official friend.
her second would be rin. even though he didn't really accepted.
so that means: yukio isn't her friend, right?
if we follow the mindset that friends don't make lover,
then it's natural people who are romantically interested in someone won't want to be their friend.
if someone is avoiding to be too close to someone else, it means that person is romantically interested. so if you try to get too close before confessing they'll think you want to be friend and when you'll confess they'll be shocked and probably turn you down. they might accept but they'll wonder why you did it this way.then,
shiemi apparently never asked yukio to be her friend
yukio most likely never asked shiemi to be his friend
and rin refuse to be shiemi's friend
what I'm trying to say is,
I can't see why would shiemi mistake love for friendship towards rin while she normally express her interest towards yukio.
I think if she was mistaking love for friendship (then for her love=friend and friend=friend so everyone are friends) she would have asked yukio to be her friend and she would have been saying yukio was her friend instead of saying she didn't had any.
*sigh*[it's hard to explain something that is so obvious to me]
shiemi is normal, she was a shut-in because of her bad health but she's still normal.
there's some things she doesn't know and she's making some mistakes.
she was too submissive to izumo's tyranny in the beginning.
still, she looks like she knows the difference between love and friendship.
maybe her love is ill placed.
but right now she seems to have a crush on yukio and friendzone rin.
I don't mind people supporting rinXshiemi but I think they should look at the book instead of the fanfiction in their head.