Cognitive Dissonance
It's not as if they don't understand what Peridot is saying. (Well, Amethyst doesn't have any personal experience, but at this point she knows enough to get the gist of it.) Homeworld's indoctrination is thorough, to say the least. Challenging it is hard. It's not difficult to spot Peridot's cognitive dissonance hard at work as she and Pearl compete. Proving that she is better at building and maneuvering her giant robot is the same as justifying the worldview she's always known. It's clear to see that losing, in Peridot's mind, will the same as finding out that she herself is defective, because of course a pearl could never be competitive—or, at least, she couldn't ever be good at it. The fault, in the end, will have to be Peridot's; anything less will be incompatible with everything she's always known to be true, no matter what.
The very fact that Pearl is so hard to best never really dawns on Peridot—just luck, Garnet can see her telling herself. Lucky shot, lucky move, the luck can't hold forever.
Let Garnet tell you, luck has absolutely nothing to do with Pearl's performance. It never does.
Garnet can see that, for Pearl, this competition is for her own dignity. She's singlehandedly reinvented what it means to be a pearl, but that's not enough—if she can't win this, then what was all of that trying and reinventing for anyway?
This is also about proving to Peridot—who is as good of a stand-in for Homeworld as she can find—that pearls, as a caste, can be so much more. Look at this, look at what I can do, see how capable and strong I am when I'm on my own—you were wrong about me; you were wrong about all of us. This is deliberate and political and deeply, deeply personal.
By the time Garnet and Amethyst approach the barn, everything the two gems are fighting for has already been set. Putting a stop to it now would be easy, but entirely inappropriate. Peridot's cognitive dissonance was bound to rear its ugly head sooner or later—and Garnet doesn't need future vision to understand this won't be the last time—but since this is all going on under Steven's supervision, things shouldn't escalate too dramatically.
Still, Garnet and Amethyst keep close, just in case. The robolympics is so entertaining that it's not really a chore. Garnet can't remember the last time she saw Pearl so genuinely fired up about something; it's nice to see she's still capable of it.
The day-long competition that still ends in a tie isn't enough to change Peridot's mind; that much is obvious. Pearl is bound to get fed up with the slander she hasn't heard in millennia at some point (who wouldn't?). They all need to work together, but it's not going to be possible to work with Peridot until she learns to give a little. This isn't Homeworld, and the sooner she understands the implications of that the better off they will all be.
Garnet has to admit, watching Pearl scream out her defiance—scream her own name like a well-deserved war cry—while punching Peridot in the face was a shock. Pearl is a lot of things, but a scrapper who deals out sucker punches is not one of them. She's usually so much more elegant than that.
She will never admit to it for diplomatic reasons, but a part of her was also cheering with Amethyst in triumph.
Of course, that punch is what breaks open the floodgates on the tension and racism that's been building up all day. Things only get worse from there, and it is decidedly not satisfying to watch Peridot's rage unfold. Garnet knows that this is Pearl's fight, and that interfering will instantly disprove Pearl's insistence that she is her own gem, belonging to nobody, fighting for herself; but it's hard to watch her and her robot slammed mercilessly into the grass. Age old instincts stir in her to jump in and stop the bullying, to put Peridot in her place, but that would only validate Peridot's worldview. She doesn't move, and doesn't speak. She just flinches every time Pearl is smashed into the grass.
"Pearl!" they all shout when she lays, dazed and groaning, in the miniature crater Peridot has created with her.
Peridot cackles as she jumps from her mecha. "Victory is mine! Now I'm the one in charge—praise me! Praise me!" She stretches her arms and grins at the sunset-painted sky expectantly.
This is Pearl's fight, and she's lost. That doesn't change what Garnet thinks of her, though—just the fact that she worked so hard is enough. The compassion and pride that Amethyst and Steven lavish on her shows they feel the same.
Amethyst is so excited that she can't seem to figure out how to react. First she screams and crushes Pearl in an enthusiastic embrace. "Yeah, P!" Then she draws back, and her decidedly less-gentle expressions of affection reveal themselves. "Oh, that was awesome—you were hardcore!" And she punches Pearl in the arm.
"Oh," says Pearl, rubbing at her bicep. She glances to Garnet, uncertain of whether she should be proud of herself.
She's fought so hard for her own dignity all day that this validation should already exists within herself; she shouldn't need Garnet to give it to her. But she's just had the snot beaten out of her, and Garnet can see she already knows how unprofessional this whole thing was, so Garnet lets it go.
Smiling, she places an affectionate hand on Pearl's head. "Oh, yeah."
The tiny smile on Pearl's face makes neglecting to point out that Garnet's opinion shouldn't matter kind of worth it. She deserves to feel proud of herself, however she gets there.
Of course, none of this acceptance and approval in the face of failure sits right with Peridot, who is still very firmly under the thumb of Homeoworld's philosophies. Her indignation and confusion-inspired aggravation are understandable. Learning curves are never easy, and things here are backwards and strange. Adjusting to any new culture is hard, and it's especially difficult when that culture is pointedly at odds with your own.
"But I won!" Peridot is practically tearing out her hair in frustration. "What about the rules?"
Garnet turns. There are a lot of things that she could say to that—grand sweeping gestures about Rose's manifesto from the rebellion, long lectures about the driving force behind the Crystal Gems as a movement, rants details the holes in Homeworld's logic and its stagnation as a culture. Oh, she could say all of that and more, but it can all be summed up in a shrug and one simple, easy statement, "Welcome to Earth."
Peridot doesn't get it at first, but then she remembers her bruised cheek, and Garnet watches the first rays of understanding break through the haze of Homeworld's brainwashing. By the end of the day, she's apologizing to Pearl for her racism. It's obviously not something she's used to doing to someone who's supposed to be in a lower caste, but she's trying, and all in all it's not a bad attempt.
Peridot's cognitive dissonance isn't gone, but it's fracturing. For now, that's enough.