Yang's Allusion
I think Yang's fairy tale allusion is criminally underdiscussed to the point that I once saw someone say it was only for the aesthetic and didn't actually inform her story, maybe because it's little more abstract (especially in comparison to Yang's role in Blake's Beauty and the Beast allusion) as it doesn't have a clear antagonist or resolution. Still, Yang's story references her fairy tale allusion in multiple ways. I am, of course, talking about Goldilocks and the Three Bears. While there are a few different versions of the tale, the most well known have Goldilocks enter the home of a family of bears, with a Mother, Father, and Baby Bear. She eats their porridge, sits in their chairs (breaking Baby Bear's), and sleeps in their beds, always finding Baby Bear's things 'just right.' When the bears return home, Goldilocks flees and is never seen from again.
Like the other members of team RWBY, Yang's story references her allusion as a whole, making particular reference to the 'too cold, too hot, just right' triad, while she herself takes inspiration from it's two most important characters. Yang is both Goldilocks (represented by her blond hair) and Baby Bear (represented by her brown clothes). She is both looking for 'just right' and already is 'just right'.
Yang as Goldilocks and the Search for 'Just Right'
While Yang may not be sleeping in other people's beds or eating their porridge, she bears other similarities to Goldilocks. Like Goldilocks she is both destructive and aimless.
Yang's semblance is destructive , both towards herself and her enemies. It requires her to take damage in order to dish it back twice as hard. She relies on anger when using her semblance and Taiyang compares her semblance to a temper tantrum. Her semblance is full of imagery to support that. She's literally hot headed, she's literally seeing red, and it's introduced in her trailer and again during initiation as a literal hair-trigger temper.
During the Vytal Festival Yang's temper is taken advantage of. Neon Katt is clearly provoking her on purpose and Yang largely wins this fight due to luck, as the terrain essentially takes Neon out. Cinder picks Yang to fight Mercury, likely because it's even easier to convince the world that she attacked Mercury after he had already lost since viewers had already seen her explode in previous fights. As both Goldilocks and Baby Bear, it's fitting that the one Yang risks hurting the most is herself (by both needing to take damage for her semblance to work and acting recklessly when using her semblance), as Goldilocks eats Baby Bears porridge and breaks his chair.
However, there's been a subtle change in Yang's semblance. There are at least a couple times in which Yang uses her semblance and her eyes turn orange instead of red, suggesting a potential semblance evolution. Namely, during RWBY vs. the Ace Ops in Volume 7 and against the Red Prince's chess pieces in Volume 9.
I believe this indicates that Yang does not have to rely on anger to use her semblance anymore. Orange as a colour is more warm instead of red hot. Perhaps it means confidence or maybe a desire to protect like Ruby with her silver eyes. I hope to see her use them more as I believe they symbolize Yang reaching 'just right' with her semblance.
Now on to Yang feeling aimless. Yang is training to become a huntress, but she doesn't feel that she has a very good reason for doing so, unfavourably comparing herself to her team.
“At least you two have something that drives you. I've just kind of always gone with the flow, you know? And that's fine. I mean, that's who I am, but how long can I really do that for? I want to be a huntress ... not really because I want to be a hero, but because I want the adventure. I want a life where I won't know what tomorrow will bring and that will be a good thing. Being a huntress just happens to line up with that. (V2Ch10)
She doesn't have a the same drive as her teammates do. She is trying to figure out what she really wants, but first, their is another question she needs an answer to. Why did Raven leave?
Yang: “(sigh) That question. Why? I didn't know the answer, but I was determined to find out. It was all I thought about.” (V2Ch6)
Yang feels as though something is wrong with her, something missing that make people leave. However, after confronting Raven at Haven and reconciling with Blake, Yang starts to heal. She realizes that she's already just right (or in other words - enough). She can keep searching for just right, but that doesn't mean she's wrong or missing something now:
Yang: “My losses, my failures, those more than anything are what have shaped me into who I am. Showed me how I need to grow. If there's something I'm missing, it's not because I've lost it. It's 'cause I haven't found it yet. And the only way to do that is to keep going.” (V9Ch4)
Yang as Baby Bear- She's Already 'Just Right'
Yang is Baby Bear, the 'just right' between her parents who are Mother Bear (Taiyang) and Father Bear (Raven).
Taiyang represents the too cold, too soft aspect of the fairy tale. The neglect he fell into due to his depression (what Yang describes as shutting-down) was so severe that Ruby considers Yang to be the one that raised her (or at least, a significant part of raising her) despite being only two years older. Like Taiyang did after losing his love, Yang seems to shut-down after the Fall of Beacon and Blake running away. She closes up to Ruby, denies her hurt over Blake, and learns to go through the motions.
Raven represents the too hot, too hard aspect of the fairy tale. Yang seems to have gotten her temper from her mother. Both their meetings in the show so far are marked by hostility. In particular at the bandit camp, Yang's eyes flash red multiple times as if she's moments away from using her semblance. Yang ends up breaking Raven's table when she speaks ill of Qrow and Taiyang. Raven's scolding, condescension, and her one save only rule all represent Raven being too hard.
Notably, both Taiyang and Raven give Yang some advice during Volume 4 and Volume 5 respectively. Yang takes this advice, but only to a point. She takes the good, but leaves out the bad. She is after all, the just right between them and is able to overcome her parents flaws.
Taiyang gives Yang advice on her semblance asking Yang to change of perspective.
Taiyang: “But you gotta keep your emotions in check. Keep a level head and think before you act. Your semblance is a great fall back, but you can't let yourself rely on it. It won't always save you” (V4Ch9) Taiyang: “You both act like the easiest way to tackle an obstacle is through it. That strength is all that matters in a fight. But if you just take a second look ... then maybe you'll see ... there's a way around as well” (V4Ch9)
When compared to Yang's fights during the first three volumes, Yang is smarter about how she uses her semblance. Before, she was often provoked into using her semblance when she either didn't need it to win (think Yang fighting the Ursa during initiation) or she didn't have an opportunity to use it yet (think Yang vs. Neon and Flynt during the Vytal festival). After, Yang is more pointed when she uses her semblance. She doesn't us it against the bandits in V4 (taking her dad's advice literally here and propelling herself over and around her opponent). When she does use it, she tends to activate it the moment before she strikes, guaranteeing a hit so none of the energy she's built up through the damage she takes is wasted. This happens in the Bees vs. Adam fight in Volume 6, RWBY vs. the Ace-Ops in Volume 7 and RWBY+J vs. The growgurt parfait-ed Jabberwalker in Volume 9.
However, Taiyang's advice is too passive. Yang doesn't treat her semblance as a fall back, the way her father views it. It's a key part of her fighting tool set, she's just more strategic about it now.
Raven's advice for Yang pertains to truth and knowledge.
Raven: “So far you've done nothing but accept what others tell you, but you need to question everything.” (V5Ch6)
Raven is active, but in a negative way. She uses knowledge to maintain control and manipulate. She advises Yang to question everything, but does not freely tell Yang what she knows. She instead tries to manipulate Yang into staying, promising answers in return. She attempts to shock Yang with a display of magic, turning into a bird (and insinuating that Ozpin had done something insidious to Qrow and Raven at the same time) and gives Yang an ultimatum.
Raven: “Stay here, with me, an I'll answer all of your questions and more. We can have a fresh start. Or ... you can go back to Qrow and join Ozpin's impossible war against Salem, and meet the same fate as so many others. But can you really go back to trusting someone that's kept so much from you?” (V5Ch6)
It's a little ironic for Raven to ask for a fresh start and warn about trusting someone that's withheld information from you before, given all the information she is withholding now (what happened to Summer, Raven), and Yang leaves.
Still, Yang takes Raven's advice and immediately starts asking questions. She even extracts a promise from Ozpin.
Yang: “If Ruby sticks around, then I will too. If there’s one I know about her, it’s that she somehow always knows the right thing to do. [a pause]. But, if we're going to help, if we're going to keep risking our lives, no more lies, no more half truths.” Ozpin (through Oscar) “Understood.” (V5Ch7)
Yang is willing to risk her life, but she wants to know why. Yang is also the most upset out of team RWBY when they learn just how much Ozpin has been keeping from them. She's uncomfortable with hiding information from Ironwood. She's the one who suggest telling Robyn about Amity Arena. It's clear that Yang doesn't just want to know the truth, but for information to be given freely. Raven holds on to information, using it gain an advantage, and to manipulate. Yang sees the same value in knowledge as Raven, but unlike Raven, she doesn't care about holding power over others.
Red, Blue, Purple-Too Hot, Too Cold, Just Right
As you may have noticed, Yang being 'just right' is symbolized by her purple eyes, a blend between her mother's red and her father's blue.
But Raven-Taiyang-Yang are not the only red-blue-purple triad. Yang's teammates also match this colour scheme with Ruby (red), Weiss (blue) and Blake (purple), suggesting that Blake is just right for Yang.
I wouldn't say that Ruby matches either too hot as well as Weiss matches too cold, but I think both of them would be the wrong partner for Blake when it comes to team RWBY.
Yang initially didn't want to be on the same team as Ruby, hoping Ruby would grow up and make new friends (and perhaps wanting a little space) without Yang to lean on. Ruby may have been more reliant on Yang and failed to learn her lesson about teamwork during initiation and Yang may have felt a little stifled with her little sister as her partner. On the other hand, I know freezerburn divorce is a bit of a joke, but I genuinely don't think Yang and Weiss would have made good partners, especially in the beginning. I don't think Yang would have put up with Weiss' shit and was happy to let Ruby handle it.
Whatever the case, Blake is the one who helps develop Yang's character best. Blake's flaw of running away preys on Yang's insecurities, but the character growth they both go through ultimately helps each other heal. Blake being purple emphasizes her role in Yang's fairy tale. There is one other thing that ties Blake to Goldilocks and the Three Bears, though. There's something interesting about the phrasing of how Blake defines her relationship with Yang to Adam.
Blake: “She's not protecting me, Adam. And I'm not protecting her. We're protecting each other.” (V6Ch11)
Her words mirror the triad structure of Goldilocks and the Three Bears, where something is wrong in two oppositional ways before finding the just right middle ground. This further ties Blake with Yang's allusion, the same way Yang is part of Blake's allusion.
In Conclusion
Yang's story is informed by Goldilocks and the Three Bears in multiple ways. Yang as Goldilocks symbolizes her desire to keep learning and keep growing. Her role as Baby Bear symbolizes her ability to overcome her parents shortcomings. The too cold-too hot-just right triad gives insight into her relationships with others. Ultimately, Yang's fairy tale allusion adds structure to her arc and is definitely not just for the aesthetic.