So! Utena thinks that Tina is an absolute sweetheart. Yeah, she's a little weird sometimes (but who isn't around here?), but she appreciates her kindness and, for lack of a better word, how safe she feels. Tina has problems, sure, but she's still a refreshingly normal girl with refreshingly normal problems, which makes it easy to relax around her and just have some fun.
However, Utena also thinks that Tina is a little immature. This makes her feel more protective of her, but it also means that Utena sees herself as a little above her, too. While she cares about her, she doesn't quite respect her as an equal; however, Utena doesn't realize this herself, and would be shocked and offended if someone brought it up.
In short, she sees Tina as kind of a little sister! She cares about her and wants her to be happy, and will try and protect her when she can, but she doesn't realize quite how capable Tina can be, either.
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However, Utena also thinks that Tina is a little immature. This makes her feel more protective of her, but it also means that Utena sees herself as a little above her, too. While she cares about her, she doesn't quite respect her as an equal; however, Utena doesn't realize this herself, and would be shocked and offended if someone brought it up.
In short, she sees Tina as kind of a little sister! She cares about her and wants her to be happy, and will try and protect her when she can, but she doesn't realize quite how capable Tina can be, either.