Yuya is a shounen female (and therefore required by the genre to not be allowed to fight a lot and to need some rescuing) whom the main character is blatantly in love with and obviously has a huge thing for almost from the beginning, who is central to the plot, and who many other characters blatantly adore, not to mention most of the cast ships Kyo/Yuya. Of course people dislike her.

Never mind that a lot of the plot is built around her even more than Kyo, and that, aside from Kyo, Aka, and Kyoshiro, you could remove any other character completely and have little affect on the plot, but you lose the plot altogether if there's no Yuya.