What a dick. He needs to learn to communicate.
Why, why, why have YOU caved in the past when he's the one being unreasonable? Why reward childish, controlling, uncommunicative dickishness - it can only have encouraged more of the same behaviour.
Tell hem calmly that his sulking is childish, unreasonable and manipulative and you are not giving to be swayed by such silliness. If he wishes to have a grown up discussion about his concerns, you are prepared to listen. Not necessarily agree, or do as he prefers but listen and talk through his concerns.
I suspect his behaviour is partly because he knows that trying to articulate his feelings would make him sound silly, so he goes for bullying tactics to avoid having to explain himself.
He needs to go through the process of trying to explain, recognising that his feelings are not the only ones that count, his perspective not the only valid one, his explanation not convincing when spoken out loud. Also that sometimes we all have to recognise that our feelings are just that, ours and feelings, not rational and not a reasonable basis for asking anyone else to behave differently.
Of course you may be able to reassure him on whatever the specific concern is. In the end either he trusts you or he doesn't.