You reach for his hand and he tenses, or he pulls his arm back before you've even landed it, or he goes still in a way that tells you the touch registered as something to survive, not receive. You're not trying to start anything. You just want to be close to your own husband, and his body treats that want like a demand.
Most of what gets written about touch aversion assumes a woman on the receiving end and a man reaching. Flip it and the mechanics don't actually change: this is still a nervous system that has learned touch carries a cost, protecting itself the only way it knows how. His withdrawal isn't a comment on his love for you. It's the same reflex that makes some people flinch and others go numb, wearing a different coat.
Why reaching more makes it worse
The instinct, when someone you love pulls away, is to close the gap. Reach again, more gently, more often, hoping persistence reads as safety. To a nervous system already on alert, more reaching reads as more pressure, and pressure is exactly what it's defending against. The gap doesn't close by you moving faster. It closes by him experiencing enough small, unpressured, exitable moments of touch that his body updates what touch actually costs.
What actually respects his limits and still moves things
Structure helps here more than warmth does, because structure gives him something warmth can't: a guaranteed end. A touch with a defined stop, agreed in advance, that neither of you have to negotiate in the moment, is the single easiest way to lower the stakes enough for his body to try it. Ask, out loud, for something absurdly small and completely time-boxed. Thirty seconds of his hand in yours, an agreed stop, no expectation of more. Let him choose the moment. Let him end it.
If talking about it tends to end in defensiveness, one prompt run properly gets further than any conversation you've had so far. Pick a single question, said out loud in capitals: "TELL ME WHAT TOUCH FEELS LIKE TO YOUR BODY RIGHT NOW." He answers, fully and honestly. You may only say "Thank you," "Clarify that," or "Summarise that," nothing else, no fixing, no defending what you hear. Then it's your turn on the same prompt. It gets you real information without either of you having to survive an argument to get it.
His limit is not a rejection of you. It's data about what his body can currently verify as safe, and data like that changes with evidence, not with wanting it to.