I have seen a lot of only anime fans (and even some manga readers, too) complain that Gon overreacted with Kite's death. They claim that Gon barely knew him, and it just came out of nowhere. Now, as a HxH fan who watched the anime first, then read the manga, I have to say that I'm not someone who thought Gon overreacted when I first watched the show. But I didn't understand the extent of Kite's true importance to Gons' character. It makes much more sense, and it is better storytelling overall even if the anime wasn't necessarily terrible either. After reading the manga for the first time, I have to say that Kite was done dirty in the anime and, to a lesser degree, Gon as well.
You see, Kite is the entire reason why Gon wants to become a hunter and meet his dad. In the anime, Gon seems to be oddly obsessed with Ging, and he is to an extent in the manga, but only because he admires Kite so much. He admires him so much that that admiration extends to Ging. Because Kite admires him so. I mean, it's only natural, right? Gon knew nothing about his parents, then one day he got saved by this random man and found out about hunters and that his dad is one of the best. Almost everyone that Gon has met who knows about Ging only says good things about him, except for Mito. So, of course, Gon is going to have some idealized version of Ging.
The anime does such a disservice to Kite and Gons relationship. They do not include Kite telling him about hunters and about his dad even though that was the entire reason why Gon went on a journey, they didn't even include Kite in the first episode, which is one of the worst decision the anime made. I guess Gon just already knows that information from Mito? I guess that means she didn't lie to him about Ging? Also the anime completely fucks up the reunion between the two. Gon never forgot about Kite and the same thing with Kite. Gon talks about Kite multiple times throughout the story, so we see how much Kite means to Gon. Kite changed his life, quite literally changed his life. And you don't get that feeling in the anime. That's one reason why his death broke Gon mentally.
Let's also bring up that Gon and Killua didn't travel with Kite for only a couple of days. It was months. 2-3 months, I believe. That's actually a lot of time to get to know someone, especially if you're traveling around.
Another reason that his death hit hard for Gon is that Kite saved Gons life twice. Once from the foxbear mother and then later from Pitou. So because of that, Gon copes with this terribly. He feels completely helpless, and he blames himself because of it. He can't do anything, and that bothers him because he was the one who was supposed to save Kite, but he failed. That also means he failed Ging. And because of all this that's happening, Gon literally becomes suicidal.
Now, we don't get much of Gons' internal monolog during the CAA, but I also interpreted his frustration with his failure to save Kite as him disappointing everyone else and himself, of course. Like Gon felt like he wasn't worthy to the people around him and that they may even leave him because of how weak he is. Because almost everyone in his life prioritized strength. And if my interpretation does get confirmed to be true later when Gon returns, then Killua and Gons separation would be even sadder because his fear would've come true. Do y'all even understand what I'm trying to say? I don't even know if I'm making sense at this point. This is why Gon is my favorite character of all time. He is so interesting and is actually so complex.
Anyways, I'm trying to explain how Kite is one of the most important person in Gons life, and people downplay it to make Gon seem like he's a crazy person when in reality he is a child who is experiencing grief for the first time. Gon was 100% valid for feeling the way he felt.
Man, this post was a bit of a mess, but I had so many thoughts about Kites' importance, so I'm sorry if this was hard to understand.
