Toph seems to associate authority with the belittling of her own importance, stemming from the fact that the original source of authority in her life - her parents - also continually condescended to her because of her blindness. As such, she has a disliking for the constraining rules of ordered society, and rebels when the constraints they put on her become too strong for her to bear while maintaining her sense of self-respect as a person. It is out of the over-concern for her own view of herself that Toph can often come off as selfish to the rest of the world, though she is not without her more compassionate moments. Earthbending seems to be the centering influence in her life, as it is the path out of the normal constraints of her "condition", and as such it is deeply connected with her view of herself. While she is almost continually questing for greater strength as an Earthbender, deep down it seems that she simply wants to be regarded as a normal human being, and so does not give up all social concerns at the outset but instead only when they conflict with her sense of self-worth (which is more often than most people). It is probably the combination of her general lack of social contact and her (depressing for a twelve-year old child) looked down-upon position which conspired together to make her want to leave her parents. They cannot be regarded as solely an obstacle to her, as she seems to be resigned at first to staying at her parents in "The Blind Bandit" when Aang offers her the chance to leave, only changing when they "tightened the reigns" unbearably (for her at least) and shut out the two things she seems to have wanted most. Her later being placed in a metal box by her two captors probably reflected on these last oppressive circumstances badly, and so Toph was driven by her position to overcome the obstacle as if it were required to prove her worth as a person- something no other earthbender has to deal with, and so none of them invented metalbending. Her outward arrogance, stubbornness, and drive for success, while not self-delusions, all stem from her uncomfortable forced questioning of her own worth.
Toph Bei Fong can be seen without her later basic tomboyish persona when she mentions her early memories in "The Firebending Masters". There she can be seen without her usual reserve, crying her eyes out in a cave, and if her later life is any indication, she probably ran away at that point because she had no way of counteracting people's low opinion of her. Once she learned Earthbending from her Badgermole "teachers", she seems to have found her fighting center, and her later tomboyishness probably stems from a need to keep herself on this track against the general current followed by most females. That being said, it is difficult to believe that at the outset Toph wishes she were a male, as she seems to have little problem joining Katara in typical "girly" activities in "The Tales of Ba Sing Se" (despite at first questioning it). Certainly, she does seem to find acting male-like to be easier, but not in such a way that it can legitimately be deemed that she hates being a girl. If anything, her tomboyish persona stems from a need to shake off the shackles of being blind, and is not a problem which originally existed alongside it. Due to her concern with proving herself worthy of equal respect as a person, period, she generally disregards the issue of her unknown appearance out of hand as a distraction from proving her worth through her abilities as an Earthbender. One's life doesn't entirely consist of fighting, however, and so it appears that she doesn't directly set out to overlook the issue of appearance as part of a set of ideals she feels she must hold herself to - though this is the general result, particularly because of the overriding nature of her true goals. It would be fallicious to place her disregard for appearances (primarily her own but probably also including those of others) and that of either as a enduring facade put up for social purposes and dropped when in private, or (on the flip side of the coin) as a stage she will fully leave behind as she grows older (considering the all pervading nature of her drive to prove she deserves to be considered equal to sighted persons); I would consider this rather obvious, but feel I must say it to counteract various ways I have seen the character written in fanonical material. Though I would generally prefer to avoid such speculation, if I had to make a choice it would appear to me from her reaction to Star-and-friends's taunts that her parents cared too much about the (assumed) physical fragility of their daughter to pay enough attention to her more mental-emotional concerns, and thus reassure her about her appearance. Surprisingly (for I do not tend to attribute more character development in "The Runaway" episode then I strictly must in order to canonically base my views on Toph), if we desire to find some solid track of character development throughout the seires she ought to be be seen as remembering how Katara reassured her after the incident with Star-and-friends (as a specific instance of what would obviously be the case in general) when she says to Sokka that Katara actually cared for the "real me" unlike her own mom. I fear what I am saying here may be easily misunderstood by one who does not share my perspectives, so I must explain this rather small point further. By the evidence I've come by, girls are predisposed to care slightly more about their appearances than guys. That being said, I understand that some girls are able to basically accept whatever they look like and shrug it off as having any meaning in their lives. With everything else we know about the character Toph, if she got the chance to simply know about her appearance (everything else about her personality and life story somehow remaining the same), she would be able to shrug it off as having any bearing on her life (regardless of how she actually looked). However, her being blind prevents her from being able to fulfill this simple curious desire, and her parent's speculated silence on the issue (because of their way of treating her more like a fragile object than a person with emotional needs) would leave her feeling slightly insecure because she cannot choose to come to a resolution on the subject on her own terms as a sighted person would (the one thing even her Earthbending abilities can't help her to overcome, to show the world she is equivalent to the group she was excluded from at birth as she would like). Her small insecurities therefore lie not in what society thinks her appearance (which she couldn't care less about), but in her inability to guage her own appearance as a sighted person would, a difference produced by her blindness which even her self-confidence level present in the series couldn't overcome by itself.
As for Toph's sense of morality when it comes to taking a life, it is indeed hard-edged. She is definitely willing to throw back at her enemies what she thinks they have thrown at her, probably undergirded by a naive sense of an "eye for an eye" justice which, however, does not generally lead to the death of her opponents (out of the self-same childish limits concerning her sense of justice). She is oversensitive (which does not necessarily imply immediate overreaction in her case) to wrongs done to her because of the threat they represent to her person, though she is willing to take this into account if pointed out to her in the correct way. With the uncomfortable memories brought up by her capture at the hands of Master Yu and Xin Fu, she punished them in kind by trapping them in the cage, most likely forgetting the possibility of their gradual death made this a far worse punishment for them than it had been for her. In the process of narrowing down what exactly she thinks she is doing, it seemed to me that her entire "dark side" is summed up in her inability to judge apart from her own learning & fighting experience (as do many others of her flaws) - what she is able to take, she throws back at the enemy; the speed at which she was probably able to learn on her feet, she attributes to Aang (even if this made his death at the hand of the boulder during her training likely); her own exciting ability to conquer the metal box she was trapped in probably blinding (metaphorically, I mean) her to the fact that she was not really paying the bounty hunters in like kind. On the opposite side of the same coin, she is shown to be able to be compassionate to those whose life-circumstances are similar to her own: expressing sympathy for Iroh when his nephew was said to have went away (similar to her leaving her parents), siding with Zuko when he wishes to join the group by saying he could have turned out worse (relating to her own difficult circumstances with her parents), sticking up for Zuko after he joined the group as the group's (former) fellow outsider, and (most obviously) generally siding with Sokka because of many similarities of personality. It cannot really be said that she is a kind, sensitive person under her hardened exterior, as this implies some sort of opposition which simply doesn't exist; rather her sensitivity plays off of her toughness and vice versa to create her general sense of morality when it comes to taking a life (as well as toward life in general).
The one time where her sense of morality doesn't seem to fall under these guidelines is during the fan-servicey episode "The Runaway" (by fan-servicey I mean written more so the fans of the show can immediately understand the plot rather than so the series would progress in a more artistic fashion). After the (supposed) training accident where Toph strikes Katara in the stomach with a rock (meant to be launched at Aang), she seems to care not a bit that her friend might be in any sort of pain, and even goes so far as to mock her subsequent complaints. After their enusing, rather cheesily-started fight, she disregards her Waterbending friend completely (with no sense that they had worked the issue out existing), and the subsequent events seem to hinge on a rift between the two emerging from this lack of amicable interaction. Though I don't particularly like making up a clearly fanonical back-story which the episode in no way directly indicates, the only way this can possibly be made to fit with her earlier and later character progression is by doing so. Any fanonical series of events which attempts to explain this must posulate an unseen off-screen event which somehow brought Toph's past life to the forefront of her mind by means of creating some argument which caused issues between Katara and her (best written, because of the former's slight - but only slight- bossiness), which for some reason the two of them were never got around to resolving. If Toph is seen as holding on to such a grudge due to a lack of a mutual understanding being reach between the two of them (unlike what was done in "The Chase"), we can at least attempt to explain how the episode starts out. Having been uncomfortably reminded of home, Toph can be seen as attempting to bury her love-hate emotional dynamic surrounding the subject of her parents by outright ignoring any moral influence they ever had on her. Understanding her actions in this way, the overall sense of morality I attribute to her throughout the series need not be thought of as fallicious; "The Runaway" simply provides an example of her lashing out without reserve because she herself couldn't handle what was going on in her inner life (which, considering her age & the nature of her past situation, doesn't necessarily mean she ought to be seen as an amoral, immature brat in this episode). Her moral reserve of limiting her eye-for-an-eye sense of justice to what she thinks a person ought to be able to handle (based on her own experience of what she was able to handle) having in this way gone bankrupt, she engages in morally questionable activities until the combination of Sokka's (mostly overcoming the immediate Katara problem) and Katara's (more directly overcoming her problem with her parents) conversations enabled her to finally be able to handle her issues with her parents. This being accomplished, the episode ends with Toph actually initiating an attempt to apologize to her parents for the pain she caused them, indicating that her earlier sense of morality has returned to her and has even matured slightly (though almost invisibly) through the overcoming of this hurdle.
(As for the often said phrase "underneath's Toph hard outer shell, there lies a senstive inner core", I wouldn't be inclined to fully agree or fully disagree. I think it was her sensitivity to her circumstances which lead her to develop her hard outer shell, and that this hard outer shell is what also leads her to be quite sensitive when it is torn down by circumstances beyond her control. So a better phrase to describe Toph would be "from sensitivity springs toughness, which brings one full circle back to sensitivity".)
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