Boyfriend says he likes holding hands and linking arms but never does it

I always have to be the one to hold his hand in the movies. And I've only held his arm twice when walking I've never tried to hold his hand because I'm afraid he'd pull away. I asked him if he doesn't like it and he says he does but he doesn't do it with me? Something's off no?
Boyfriend says he likes holding hands and linking arms but never does it
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