HE IS A LEWD GODDESS!
Rikkun said that all he saw in his <Presage> was a funeral with Kristoff's name and picture on the coffin. There are no other details about his incoming death. I guess Rikkun's Guardian Ability is just good in giving hints on some future events.
But still, we have to ready ourselves in the tournament. We have to train hard in order to win the God Core and also prevent Kristoff's death (provided that he will not die due to uncool ways such as road accidents and diseases.)
The Aether Crusade is divided into two teams: The Tournament Team, which is led by Kristoff, and the Investigation Team which is led by Rikkun.
It is only logical for us to pick Mister Kristoff as a leader because he has more experience in battling than any of us. I may have been a Gate Guardian longer than he is, but I've been shut from the outside world until I turned sixteen. Kristoff already fought Eidolons when he was at his early teens, and he's really strong and smart!