Fur, or hair, on an animal, like the pile on a knotted rug, or the grain in wood, flows naturally in a given direction. Working against the grain is the same as brushing a cat from his rear-end forward to his head, or vacuuming a rug against the lay of the pile, or 'rubbing me the wrong way' (that's the common way of saying it)-- means 'to irritate'.
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