Ok, so she's a
more shallow and boring version of Sakura, she's a Mary Sue, her personality is like a cardboard box, she treats Eren like a little kid and she generally sucks.
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First off, Mary Sues are considered one-dimensional because most authors never throw any meaningful conflict, or obstacles in their path that allot for any sort of character growth or evolution. Quite literally, Mary Sue gets everything she’s ever wanted without EVER having to truly work for it. She usually does this by getting each and every character to like her unconditionally with her Aura of Smooth.
If Mikasa was a Mary Sue, Eren would NOT have headbutted her in episode 5 and told her to get her shit together. He wouldn’t have popped out that line in episode 10 either “I’m not your brother nor am I your child!”. As a matter of fact, Eren and Mikasa share this mutual relationship of calling each other out on their bullshit. Mary Sue wouldn’t allow that from her supposed “male interest” because Mary Sue expects you to eat up every hunk of BULLSHIT she throws your way and then wait for you to dutifully ask for seconds.
In episode 7, Mikasa tried and failed epicly to give a motivational speech to her disheartened peers. Remember that? It was Jean who actually got them off their asses, not Mikasa. Mikasa has no charisma with other people whatsoever. Hell, she can’t even sway Eren—the guy she’s in love with.
While it’s true that Mikasa is strong in some ways, shes astronomically weak in others. Take for instance, her devotion to Eren. In episode 8 we see her monologue about how although she led her comrades into battle she did not accept responsibility of their lives. Instead she abandoned them and her reason to live, all for personal reasons. Also in episode 22 when her and Levi are fighting the female-type titan she ignores Levi’s warning and her good judgement in favor of letting her anger and her desire to take back Eren control her. Hence Levi’s injury.
Case in point, for all of her worth as a solider and child prodigy, she is in fact, still a human w/ flaws. Don’t let that calm demeanor fool you, she’s not emotionally stable nor is she always capable of exercising good judgement (as much as she likes to believe otherwise). And it’s this balance in strength vs weakness that exempts her from the role of Mary Sue—a character that’s always depicted as perfect and in the right no matter what [like Itachi]. Mikasa may be good at killing titans but where Eren and her priorities are involved, she couldn't be any more inept (or clueless).