Summary
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Aoi Todo pushes his friends to excel, trained by Yuji during the Kyoto Sister School's Goodwill event.
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Todo defends and defends his friends and stands up for Yuji against his fellow Kyoto students.
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Todo supports his friends' emotions and helps Yuji overcome his grief during the Shibuya incident.
This feature contains spoilers from the Shibuya Incident in arc Jujutsu Kaisenseason 2
Aoi Todo bursts in Jujutsu Kaisen with such bombast that it's hard to get the hang of it. Who asks a stranger they just met what their taste in women is? What about his idol crush? Is this dude a carnivore, or is there more going on beneath those muscles? All of them Jujutsu Kaisen the characters are multi-layered, with Todo being one of the most complex.
Todo begins an initially one-sided friendship with the confused Yuji Itadori. However, as the pair's friendship grows, Todo repeatedly shows his honor and loyalty. Later, Toda's strength of character and emotional intelligence save Yuji from what could quickly become execution at the hands of Mahito. In short, Aoi Todo is one of the best friends you can have.

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Todo pushes his friends to strive for more
The Kyoto Sister School Goodwill Event reveals a lot about the character of each Jujutsu High School student. However, the most commendable display of sportsmanship goes to Aoi Todo, who enthusiastically takes Yuji under his wing (even though Yuji is initially disinterested).
Todo trains Yuji using the Black Flash technique, a rare physical attack that wizards can occasionally perform under certain circumstances. It's basically the wizard version of “being in the zone”. After noticing the lag between Yuji's physical strikes and the cursed energy that characterizes his Divergent Fist technique, Todo challenges his new friend.
A 1st-level Magnificent Wizard will not accept mediocrity, especially from those he cares about. In Season 1, Episode 15, “Kyoto Sister School Exchange – Group Battle 1 -“, Todo gives Yuji an ultimatum:
If you are content to stay at this level, then unfortunately you and I cannot remain best friends
Yuji accepts Todo's help and the two split up while Todo teaches Yuji new lessons about cursed energy flow. When the Psuedo-Geto compatriots invade the Tokyo Jujutsu High campus, Todo's coaching allows Yuji to unleash a black flash on Hanami, a dangerous cursed spirit of a special class.
Todo defends his friends
When Todo forms a bond with someone, nothing can come between them, not even Todo's allies. After Toda's first round with Itadori in the “Kyoto Sister School Exchange Event – Group Battle 1 -“, his classmates from Kyoto interrupt the pair's sparring. Although the Gakuganji headmaster orders his students to kill Itadori, Todo defies these wishes and tells Noritoshi and his peers to back off. Toda's willingness to defend Yuji even against his classmates is admirable.
Todo gives Yuji personal respect. However, the best diagnostic of a friendship is how said friend talks about you when you're not around. Nothing crushes the soul more than a two-faced lunatic who sings your praises to your face only to insult you behind your back.
Fortunately, Todo is 110 percent honest. He will never lie to your face and always defend you behind closed doors. The ending of Series 1 exemplifies Toda's commitment to Yuji. After witnessing Itadori's potential during the Goodwill Event, he decided to recommend Itadori for promotion.

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Todo gives space to his friends' emotions
The most significant turning point regarding Yuji and Toda's friendship is during the Shibuya incident. Even the best of friends struggle when faced with grief, either dismissing their friend's feelings or being so overwhelmed that they allow the relationship to fade. As Todo witnesses Yuji grieving over the many victims of Nanami, Nobara, and Sukuna, the audience knows that his reaction can go several ways.
Aoi Toda's macho-man archetype may lead viewers to expect him to scold Yujima. Maybe he'd give a cheeky, “Stop feeling sorry for yourself” speech. However, Yuji doesn't need that now. Instead, Todo calmly talks to Yuji, leaving room for his friend's deep despair. Todo's words acknowledge Yuji's love for others and channel that love in a more productive direction.
Brother, you are a man among men. Don't limit yourself to such a limitation.
Then Todo moves his words towards progress. He reminds Yuji that being a jujutsu wizard is unpredictable and relieves him of the guilt that is too much for one person. In the end, Todo directs Yuji to action and encourages him to keep fighting so that all the victims of the Shibuya incident are not in vain.
Trying to find meaning in the death of the fallen can sometimes taint the memory of those we have lost… What has been entrusted to you?… Until you can find it, you cannot stop moving forward.
Toda's reasoning adjusts Yuji's perspective and allows the young man with a big heart to continue fighting. This comeback cements Yuji and Toda's friendship. In Season 2, Episode 45, “Metamorphosis”, Yuji takes over the battle against Mahito. As the young wizard leaves, he expresses his gratitude and calls Tod his brother. If only everyone were lucky enough to find a “brother” like Todo.