I sit next with this girl nearly half of all my classes. Not just in the same room, but right next to each other. At first, I thought of just starting a relationship, but she is deathly quiet all the time around me. She would not talk to me at all, but rather someone all the way across the class. Even though we see a lot of each other every day, she always seems to sad. I can't tell whether she is really introverted, or if she just really hates me...

What do you think?

Maybe neither she hates you nor she's introverted. Maybe you feel this way because you are focused on her. She probably sees you as just the kid that sits next to her. Like are you as concerned about the other kids that sit next to you not giving you any attention? Is she giving the other guys that sit next to her any more attention than she gives you? I'd say you are looking for attention and she is just trying to be a normal student.

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Have you actually tried speaking with her? Why do you expect her to talk to you, if you never say anything? How about Hi, how are you today?

You think she is a mind reader or something?