To be a source of irritation to one. Of course he would lie and take all the credit for my idea—he wanted to have it stick in my craw!See also: craw, have, stick
have (something) stick in one's craw
Fig. to have something irritate or displease someone. I don't like to have someone's words stick in my craw.He meant to have the problem stick in my craw and upset me.See also: craw, have, stick