Kaido was a kid when he saw the Rocks war vs. Garp and Roger. This was probably the greatest war in pirate history, even greater than Marineford. But that's the thing. He was a KID. That means he couldn't be a big shot like Roger, Whitebeard and Rocks, and was relegated to a passenger role.
Big Mom reminding him that he owes her a lifetime favour is probably her saving his life in this very war. Kaido even says "that was a long time ago", and Big Mom reminds him that it's something that can never be brushed aside.
But, now that Kaido is the strongest creature in the world, he wants to relive the great war, but this time be at the CENTER of it, and not just a passenger like he was when he was a kid. He wants to die a "great" death like Rocks.
Big Mom reminding him that he owes her a lifetime favour is probably her saving his life in this very war. Kaido even says "that was a long time ago", and Big Mom reminds him that it's something that can never be brushed aside.
But, now that Kaido is the strongest creature in the world, he wants to relive the great war, but this time be at the CENTER of it, and not just a passenger like he was when he was a kid. He wants to die a "great" death like Rocks.