Irritate, annoy, as in His remarks about welfare rubbed a great many people the wrong way. This idiom alludes to rubbing an animal's fur in the wrong direction. [Mid-1800s] Also see ruffle someone's feathers.
To annoy; irritate: "One can see ... how [his] expression of his ideals and intentions must have rubbed many people the wrong way"(Christopher Lehmann-Haupt).