There are many reasons the fandom has explained away why, of all his Guardians, TYL!Tsuna only told TYL!Kyouya.
Whether it's because he has the Foundation, rarely interacts with the Main Familia, or just that he's a Cloud - there are a lot of reasons.
There's also the ones about how TYL!Kyouya would be the only one to keep a clear head when TYL!Tsuna has just died, how he's the only one both cold enough to be steady enough to train Tsuna, but cares enough to actually do it.
There's also the shipping ones, how TYL! Kyouya is the only person TYL!Tsuna both truly knows and cares for, how he knows his lover will train his younger self.
I think this can all be true, but there's also something else. Of all his Guardians, Kyouya is perhaps the only one that doesn't expect Tsuna to do things he doesn't want to do that doesn't benefit him. Nor forces him in a role he does not want.
Gyokudera, from his first interaction with Tsuna, revolves around the fact that Tsuna will be Vongola Decimo. It's likely, even on their deathbeds, he will call Tsuna Jyuudaime, and even after that. Tsuna will never actually be able to be himself around him, especially once he's truly Vongola Decimo.
Takeshi will always seen Tsuna as the boy who saved him from suicide, who gave him a purpose. Tsuna gave Takeshi his Will to live - and this colours all their future interactions.
Lampo is the kid he took in, who looks up to him, who he always has to be the role model to.
Ryouhei is always so bright and genuine, dragged into the Mafia only because he's the strongest Sun Namimori has.
Chrome has always called Tsuna Boss. While she may be one of the few he actually would've truly Harmonized properly without outside influence, their relationship has long been tainted by outside perspective and opinions long before they met.
Mukuro is another he would've naturally Harmonized with, without tampering. Still, Mukuro doesn't try to bond with Tsuna. Can't, when he's been in Vindicare for so long in the TYL.
Kyouya is the only one who both never forced him into the Mafia nor anchored him as his Will to live. Tsuna is simply the Sky his Clouds drift through. It's just as simple and as complicated as that. Kyouya just wants Tsuna strong enough to both protect himself and to be a better sparring partner. Kyouya doesn't care if Tsuna is a Boss or a Lackey. In the end, Tsuna will most likely always be Little Animal in Kyouya's eyes.