It seems to me that he’s not taking the game seriously. But that’s kind of ok, there’s plenty of ways for the GM to push around the character, and help make the player more interested in what happens to it. He had the Roden cultist just walk out of the room? That means he’s not getting paid. How do his fellow cultists feel about that? How do they feel about him leading a bunch of folks down to their super-special sword and just letting them walk out with it? Is he even gonna make it back out of the tunnels without the rest of the gang? Maybe he doesn’t care what happens to the Roden because he had him do that, but maybe he wants to see what would happen if he did something really unexpected.
If you guys are playing a bunch of 1 on 1’s, maybe he thinks he’s doing you a favor by trying to break the game like this. Maybe he’s trying to get you to react more spontaneously to when he does things with his character one plainly wouldn’t expect, given its beliefs, traits and instincts. IIRC, there’s mechanical consequences whenever you do something relevant to your beliefs, whether it’s upholding them, or violating them. So he’s violating beliefs by walking away from encounters? Give him his consequences. If he’s arguing with you over whether there should be consequences for his character doing or not doing something, then he’s not interested in playing the game. If he’s arguing with you over what those consequences should be, then he’s invested. I rather suspect, though, that given his “its just a game, dude. Chill out.” response, he’s not interested in playing. I could be wrong though.
Did you try him on Guiding Light beliefs? (Non-goal beliefs like “everyone deserves a second chance” or the like, which are written to earn Fate rather than aimed at Personal Goals artha.) Especially in a one-on-one game, one or two goals and the rest Guiding Light might easily net you more artha than three goal beliefs (since you won’t likely achieve all three each session and you don’t need the versatility to work around other players’ goals and needs.)
The problem with that is that one of his other beliefs is already a Guiding Light belief. To have two of them would be… eh. I dunno. I don’t like too many of those beliefs.
Some people just have a lot of trouble writing good beliefs. I have one player who sometimes plays with only 1 or 2 beliefs. He went three sessions with zero instincts too. It’s not so much of a problem, he just doesn’t get the spotlight as often as the others, and doesn’t earn as much artha. I try to help him as much as possible, but I’d rather get the story rolling than waste hours humming and hawing.
And in a one-on-one campaign, he’s gonna get the spotlight anyways, so don’t worry about it. He’ll think up a third belief soon enough. Just make sure to have story events that give him enough belief fodder to fuel his imagination.