OP, I don't know jack about "Cassandra Syndrome" - so I can't speak to that. However, I think I can shed some light on what's going on with this girl.
From her perspective, she probably thought you were playing some heavy-duty mind games with her. As you stated, you both got along well, flirted with each other, and communicated well enough that you realized she would have welcomed an invitation to date. But you never extended that invitation.
You know you didn't extend that invitation because you just don't know how to do that. But she has no clue as to why you didn't ask her out. She probably wracked her brain trying to figure out what was going on: did she completely misread you; did she completely misunderstand your intentions; instead of the nice guy you seemed to be, were you just trying to mess with her; did you not like her romantically; are you gay....the possibilities are endless. All she knows is that she liked you, she thought you liked her, she gave you "the signal" to ask her out, and you never did. To top that, you didn't blow her off, and maybe you didn't really act any differently toward her in class....you just didn't ask her out.
So she's left wondering, with a lot of doubts about you, about herself, about why you treated her the way you did - its not a good position to be in. If you really care about her, I think you owe her an explanation. Clearly, you understood that she was frustrated, you understood that she was making all kinds of efforts to engage you - and you chose not to tell her what was going on. That kinda sucks, OP. Even if you couldn't find a way to speak to her about it, maybe you could have written her a note. So, I think you need to figure out why you chose not to tell her what the problem was (knowing that would have at least provided her with a context to understand your behavior). I encourage you to do that soul searching prior to talking to her (if you choose to do that), so that you can take responsibility for your own behavior.
Also, I encourage you not to assume that this girl loves you. I understand that you're associating the look she gave you with the look your mother has given you, but the commonality of that look does not equal love.
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What you feel is what you are and what you are is beautiful...