Tobio Kageyama and Grief
disclaimer: I haven't read the manga in a while, so do correct me if I'm wrong. This is my interpretation.
Karasuno unknowingly healed Tobio's grief of losing his grandfather, Kazuyo.
Tobio is so, so, so full of love, and it was Kazuyo who was the only one to truly understand him then. It's not as simple as Tobio losing Kazuyo---though the death of someone so beloved is hardly ever simple---but rather, Kazuyo was his whole world and volleyball was the way in which they connected with each other, more so from Kageyama. So Kazuyo's death felt as if Tobio's connection with his grandfather was severed.
In the panels when Tobio visited Kazuyo in the hospital, and the funeral, and him not getting into Shiratorizawa, he wasn't crying. He spoke nothing. He made no indication of grieving in a way that others could see. It was simply an empty, dull expression. His grief was silent. It was as if the world had stopped.
Kazuyo promised Tobio that if he [Tobio] did not purposefully limit himself on the court, be it his skills or his hunger for more volleyball, he would eventually find his "somebody even better." If Tobio did not hold himself back, then he would undoubtedly find someone just as crazy about volleyball and have the same hunger and drive to remain on the court; someone who not only loves volleyball but lives and breathes it, as if it's the most natural thing in the world---like him.
As if to attempt to fulfill that promise as quickly as possible, as if to find that spark and that familiar connection once again, he sought it with desperation. (paraphrasing) "Why are you so slow?" "Why are you not going for the ball?!" "It doesn't matter if we're leading in the game, you cannot give up on the ball!" His complicated expressions, abrasive tone, and all the problems that came with it eventually resulted in him being dubbed The King of the Court. Tobio simply wanted to be understood, but his teammates could never fulfill that promise because that special someone is not anyone of them.
(I just want to say that Kitagawa Daiichi's players were NOT wrong in not wanting to play with Tobio, even though my heart is sad to see Tobio alone.)
To other players (specifically Kitagawa Daiichi), Tobio came off as arrogant because he IS extremely skilled, but a prickly personality and incompatibility (in many ways) with the team did not help, so they (reasonably so) thought that Tobio looked down on them because they did not and could not match his speed and skills. But to Tobio, he was merely trying to do what Kazuyo promised. Relationships were strained on all sides. We have a boy who is grieving in silence, trying to fulfill a promise, grief-stricken, and boys who don't know.
That is, until he met Shoyo Hinata, and the entirety of Karasuno's boys' volleyball team. (I have so much to say about how EVERYONE took part in Kageyama's growth, but that's for another time.)
Yes, Hinata indeed fulfilled that singular, specific promise, but it wasn't JUST Hinata who made an impact on Tobio's life. Karasuno, from the players to the managers, to the coaches, and all those who came to support their games (looking at you Saeko), they unknowingly built a home for Tobio. The connection is not the same as the one Tobio had with Kazuyo, but it's there, and Tobio is always welcome to be in that space as he is surrounded by people who care and understand. Karasuno, as a whole, reconnected him with his grandfather by fulfilling that promise.
His grief remains, but he's no longer alone. He found a lifelong partner. He found strong teammates. He found a community. He found strong players at the highest stage and across the world. Tobio's love and the grief of Kazuyo's death will always remain with him, but now, these new connections have allowed him to take a step forward. Kazuyo's promise came true---THEIR promise came true---and how wonderful that is.
"Why are you even here? So you can have some fun memories of your last year?" vs. "I wanted to take this team further" vs. "I know, now. All of you taught it to me, so I know it must be true!"
Volleyball is connection. Connection is love.