Of the students, Kaorin is definitely my least favorite. She's awkward, and primarily defined by her crush on Sakaki. On the other hand, she's at least more interesting than Nyamo (in my opinion, anyway). The huge difficulty in analyzing her is that she's almost never doing anything that doesn't involve acting like an idiot in front of her crush. We simply don't get to see her at her best, or know anything much about her.
Most fanfiction writers who pair like to pair her off with Sakaki, making it so that she achieves her lofty goals of catching her classmate's attention. Why do people do this? Maybe they feel sorry for Kaorin. Maybe they just like gay fanfiction. Or perhaps they identify with Kaorin, because her struggle reminds them of times in their past when they were too afraid to get what they wanted. Maybe by giving Kaorin what she wants, it'll feel like a cathartic way of having that thing the fanfic writer missed out on.
But you know where they aren't getting this pairing from? The show.
I mean, holy crap, Kaorin is the dictionary definition of awkward. Do you see how she acts in front of Sakaki? Sakaki is too reserved to do much about it, but do you really think she doesn't see how ridiculous Kaorin gets? Kaorin is forever staring at her in class, and always freaks out if it looks like someone else is attracting Sakaki's attention. She says weird things all the time, too. Like when they were about to go on the third summer vacation, and apparently the thing Kaorin says to her when she arrives is something Japanese wives say to their husbands right after they marry. And the folk dance, when she won't let go of Sakaki's hand? What is Sakaki supposed to think about that?
The absolute worst was during the three legged race in the second sports fest. Let's count all the ways Kaorin makes a fool of herself.
1. freaking out when Sakaki is drafted into the event.
2. growling at her best friend when Chihiro suggests she could do the race after all.
3. making panicky promises of trying her best before the race starts.
4. completely losing her mind when they win.
5. suggesting they remain tied together afterwards.