These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Yozora's mean streak and selfishness are obvious, but almost all of her bile seems reserved for Sena and Maria, the arrogant RichAlpha Bitch and Insufferable GeniusBratty Half-Pint. As the series goes on, she starts getting the hints of when she goes too far in her Break the Haughty hobby, as when she pushes Sena too far until she passionately admits her devotion to Eroge in such a way that even Rika is shocked. Yozora honestly apologizes.
Some fans theorize that Yukimura's obsession with being "a true Japanese man" may indicate being a female-to-male Transgender.
With Volumes 7 and 8, there's a Broken Base among the shippers as to whether Sena's storyline is "peaking too early" (in harem series, a sure sign of a Romantic Runner-Up) or not. As of the end of Volume 8, the heavy focus on Sena is lampshaded, and Volume 9 seems to be leading into a Yozora-heavy storyline.
Foe Yay/Les Yay: There's something more to Yozora and Sena's relationship than their frequent squabbles would indicate. On Yozora's side, she believes nicknames are only for friends, even if it was as insulting as Sena's "Meat". On Sena's side, she confessed to Kodaka that she's secretly happy with her nickname because she has never been given one before. Then comes actual interaction: during the Beach Episode Sena was apparently enjoying Yozora rubbing her back with suntan with her feet, and also commented that Yozora, post-haircut, looks ridiculously handsomeon a male school uniform. Not to mention Sena plastering her bedroom ceiling with pictures of Yozura and the shots of her smelling Yozura's wig with her hand between her legs!
Sena and Yozora are both unpleasant people who don't give much consideration to others, and can often be outright intentionally cruel, malicious, or vindictive. But you can't help but feel really sorry for them every time they accidentally say or do something that highlights that they're just really lonely people who want to make friends but don't know how. Well, that and they tend to suffer amusingly for their own behavior.
Yozora's woobie status seems to have kicked into high gear as of the end of Volume 9, as the reasons for her dislike of romance and same-sex friendships are laid bare (her mother's best friend betrayed her by having an affair with her father), and is shown to have a dysfunctional relationship with her sister Hinata as the two took opposite sides in a bitter divorce. Needless to say, Sena's confession and Kodaka hiding out with the Student Council in Volume 8 didn't help, nor did her overhearing Kodaka and Rika's conversation at the end of the volume.
Running the Asylum: An incredibly fast example, as the alternate "Plus" manga has already started up, and seems to be written by a Kodaka/Sena shipper. Though it's only begun to be translated, it already seems to be working on turning Yozora into an even bigger bitch than before. The Die for Our Ship elements are particularly jarring given that Yozora wasn't comfortable with the concept of romance in the first place, and wanted to be just friends anyhow. Thus it was a ship that sunk itself.
In other parts of the vast reaches of the internet, there's a battle brewing between those who prefer to see Kodaka with Yozora, and others who would rather see him with Sena. The other girls are largely relegated to Demoted to Extra status in this regard. Amusingly, Kodaka himself keeps letting it slip that Rika is really his type (or would be with a better personality, but that goes for all the girls).
If the events of volume 8 go unobstructed, seems like the joke's gonna be on Yozora fans. As of volume 9, the Sena ship has effectively been halted with a torpedo, letting the other ships close in, since Kodaka turns down Sena's offer of marriage.
Rika and Yukimura's ships seem to be gaining some steam with the second anime season. Volume 9 does little to stop them.