Ask him why becoming a hero involves letting your master (and the possibility of proper wings) die.
Dragon: "Will my master die if I go with you?"
Captain: "It depends on how you alter the lives of his ancestors, I assure you that your life will be fine whether or not he exists."
Dragon: "Then what's the point of offering to let me continue on?"
Captain: "There are things you need to do in this time as well, you'll find out what that'll be soon enough, but the order will not matter."
well noxia loving hates the professor so if you tell her you killed him she might want the D
You are pretty sure she already wants 'the D'.
What if I choose to do something other than those two options?
Captain: "Your fate is already decided, someway or another, you'll end up on each path. You may even ask the dragon gods themselves if you doubt it."
Dragon: "Wait, you spoke to them?"
Captain: "Why of course lad! They're one of the most closest beings to this planet."
Dragon: "I see. May I try to save my master before I follow you?"
Captain: "Sure thing, the sooner you begin the better it is for everyone!"
Captain: "Have a pleasant rest, lad."