Ok seriously he is her first cousin i dont know why she has a crush on him. I dont understand her relationship with him. She had crush on him because she didn't know that kirito is her own cousin. She had a crush on Kazuto before he entered SAO, when she overheard that they weren't actually siblings, but only realized that it was a crush while he was in the game. When he woke up from the game, she found out that he was in love with Asuna, figuring that he felt that way about her due to the game. That's when she secretly began playing ALO to try to understand what he went through, eventually using it as an escape from her feelings. She eventually met Kirito in the game, unknowing that it was actually Kazuto because she never knew his in-game persona prior and developed the same feelings for him due to it being the same person. As to WHY she allowed herself to develop such feelings for a cousin, well, the laws on marriage in Japan are more lenient with familial relationships, depending on the circumstances. Brothers and sisters are right out, but second cousins are completely fine, no questions asked. But with first cousins it gets complicated, and I'm not sure I fully understand it.
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In the real world, Suguha is the cousin and adoptive sister of series protagonist Kirito ; after he becomes trapped in the eponymous Sword Art Online video game in the series' first story arc, she starts playing Alfheim Online due to its similar nature to better understand the world in which her brother is imprisoned. After her mother reveals to her that Kazuto is not her biological brother, Suguha starts to develop romantic feelings towards him, though is later saddened after realizing his attachment to Asuna. The character has received mostly positive critical reception, with praise centred on her character development, attractiveness, and portrayal. Suguha, also known as Sugu, is Kirito's "sister" in the real world; she is in actuality his cousin, as her mother had been raising her sister's child from a young age, though neither Suguha nor Kirito knew about this until later. This causes Sugu to develop feelings for him that she doesn't really understand;  however, because he is trapped inside SAO , she never acts on them. That being said, when Kazuto awakens after his two-year ordeal, those feelings come back, but she realizes that he is already in love with someone else, namely Asuna.
Suguha is the cousin and adoptive sister of Kirigaya Kazuto , but was raised along with him as his sister. In order to protect Kazuto from the wrath of their grandfather when he decided to quit kendo, Suguha became an accomplished kendo practitioner in his stead. Suguha has short black hair and dark grey eyes, almost blackish. Due to her kendo training, Suguha has strong and defined muscles that show up even when she makes small movements. Suguha's three sizes are  in the web serialization. In ALfheim Online, Suguha appears more like an adult than a child. She has bright green eyes and wears white and green clothes. She also has a white and green collar on her neck.