Okay Isabelle Lightwood mini-essay because she's everything to me.
I think that more so than the other Mortal Instruments characters, Isabelle is defined by her relationships to others. That's hardly a bad thing, and I truly adore her, but Isabelle has very much been shaped by her parents, her relationship to her brothers, and then her romantic relationship with Simon.
Isabelle has known since a very young age that her father was unfaithful to her mother, which has given her a very cynical view of romantic love. She sleeps around, mostly with Downworlders and mundanes because her parent's wouldn't approve of that, but she believes that she couldn't ever trust or fully love someone. Despite the relative experience (we're told) she has with romance, she has very little experience in emotional authenticity in such relationships.
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The people that she does openly love and trust, though, are her brothers. Her most important relationship in the series is with Alec. Alec has spent a lot of his life trying not to be noticed, and Isabelle has adapted to be this big, flamboyant personality to take the attention off of him. She does everything she can to draw the attention (and even ire) of her parents, not because she strictly wants their attention, but to keep their eyes off of Alec, so that they don't notice his queerness and potentially reject him. Alec is the oldest, but he and Isabelle are in this slight conflict where they each feel responsible for the other.
I think that both Alec and Simon are correct here, though the narrative is more interested in Simon's (incredibly insensitively worded) assertion. I also think that Isabelle doesn't necessarily feel that she has to prove anything because she's a girl, but more because of the poor reputation her family has after her parents were in the Circle.
Being the child of people who were formerly in the cult of a genocidal maniac can't be easy. Her resentment towards her father (and probably towards her mother for staying with him post-cheating) and the general negative reputation her parents gained from their involvement in the Circle, combined with her fear of how others will perceive her brother for being gay, means that Isabelle even automatically assumes that anyone who is speaking about her family is viewing them negatively.
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Returning to her brothers, I wouldn't say that Isabelle is maternal toward Max, who is so much younger than she is, but she does feel responsible for him, too. And when she fails to protect him and he gets killed, she takes on the responsibility for it. She takes great pride in her demon fighting skills, but that wasn't enough.
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And while we don't see much of her relationship with Jace, I think it's clear that Isabelle worries a lot about Jace's self-destructive tendencies and, in tandem with Alec, has to work overtime to keep Jace from hurting himself. She takes on a lot of responsibility with regard to her siblings, and though she has this outward brashness, even silliness, internally, she's become very hard, and she struggles a lot with authenticity in her feelings towards anyone other than her brothers.
She has also very much internalized the values of Shadowhunter society. She views herself as a warrior, someone who should be able to handle anything. And because of the events of the series, she's wrestling with the reality that that isn't the only way to be for the first time.
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And, notably, Isabelle has no close female relationships. She has a strained relationship with her mother and has grown up in an extremely isolated environment, where the only people she knows are her parents, her tutor, and her brothers. Clary is this big question mark to Isabelle, both in Clary's literal between-worlds status and questionable parentage, and in that Isabelle isn't entirely sure how to behave around girls her own age.
Despite the Lightwood's isolated upbringing, both Isabelle and Alec are repeatedly contrasted to other Shadowhunters with regard to their attitude toward non-Shadowhunters. The Lightwoods, especially Alec, are still guilty of a certain amount of anti-Downworld sentiment, but they are much more comfortable with them than almost anyone else. Because they were raised in New York, not Idris, they have a much wider worldview. Of all of our Shadowhunter characters, Isabelle expresses the least amount of anti-Downworld bigotry.
Underneath all of this pressure and her false, bubbly exterior that starts to erode after Max's death, she's still a teenage girl, but, because of all of her emotional repression, she can't really accept help or comfort from anyone other than Alec or a complete stranger.
And she gets this wrench thrown in her worldview when she accidentally falls for her latest "inappropriate" boytoy (Simon). Where Isabelle is guarded (as are most Shadowhunters), Simon is very emotionally authentic, and that is strange to her. She almost can't believe that he truly feels the way that he says he does. Or that she somehow fell for a scrawny, nerdy mundane. Isabelle and Simon are paired off romantically as early as the first book, but their relationship is uncertain for almost the entire series. Where Clary/Jace and Alec/Magnus are in deep from the beginning, Simon/Isabelle are a bit of a slower burn (not that slow, considering the breakneck pacing of this series, but still) and only fully get together at the end of the last book. They both have a lot of growing to do before they're actually very compatible, and it takes quite a lot to break down this barrier that Isabelle has constructed around her heart, to give this unlikely subject of her affection the power to potentially hurt her the way that her mother was hurt.
City of Lost Souls chapter 12:
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I think that Isabelle's overall arc is summarized very nicely in her visit to the Iron Sisters in City of Lost Souls. She meets these women that are much like her: strong, fearless, skilled, but self-isolated and cold. But this is relatively late in the series, and by this point, Isabelle can see how pointless this hardness is.
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Much like Sister Dolores, Isabelle became more isolated after being hurt and experiencing loss (first learning about her parent's relationship, then losing her little brother). But instead of embracing this shell, this soldier that she's been raised to be, Isabelle emphasizes her own humanity, her connection to others. Because that's what's most important.