[He doesn't want her to worry! She has so many people to worry about who aren't him! With some forced levity:] Try not to be too sad. I promise that, if I feel that I need to unburden myself, you will be the first person I turn to.
[That's... actually the truth. Chekov relied too heavily on Korra's companionship when he first arrived and hasn't opened up to many people; Kitty's the closest friend he has right now.