@BOTMAN
It's two separate choices; First one is "does he give a cure to the chairman?", yes he's able to but he only has 5 of this miracle cure left and if he cures somebody else then he's going to get more and more requests for it. He can't cure the entire world with this stuff, he has to be extremely careful & selective with when and why he uses these miracle cures as he can't get more of them, but other people wouldn't understand that if they see him able to cure some people.
The other choice is about his sister / family, his sister is terrified at the idea of monsters and doesn't want to lose her brother. Sure Jin Woo is strong enough to handle some giants but his sister doesn't know that, if he goes to Japan to fight this dungeon breach then his sister will be worried sick the entire time, whereas if he stays here at home she will be reassured. The question is his sister's happiness & well-being more important to him, or are thousands of lives he doesn't know from another country more important to him?