Say what you will, but this man is someone I want to be with (no homo) if ever I'm stuck in a deserted island. Helping out others with no hesitation might be a bit idiotic considering their current supply status, but it certainly commendable on a human level.
I think it's partially him wanting to try out every tip and trick he has learned from watching survival videos. For him it's like an amusement park, especially with the random reverse isekai'd waifus dropping on the island. The dude clearly has been itching for this type of action.
Also it's not like the dragon is dead weight, if they manage to rescue her. She's a heat source and can generate scales/claws which are very useful in such an environment.