What is the origin of the idiomatic expression rub someone the wrong way?
Is it correct to use the idiom in reverse, i.e. rub someone the right way, possibly meaning to calm or to please?
The New Oxford American Dictionary has:
rub someone (or Brit. rub someone up) the wrong way: irritate or repel someone as by stroking a cat against the lie of its fur.
So clearly, the origin is that of stroking a cat: cats like to be petted from head to tail, rather than in the opposition direction.
For your second question, It does exist: rub the right way but I have only seen it as a word play on rub the wrong way. It does not feel like an official antonym to rub the wrong way
There is this early reference to cats:
"Very probably," said Henry, smiling at poor Charles's credulity, "for nothing is more likely to resemble a cat than one of its own species; and I know, that when a cat's back is rubbed the wrong way, sparks, which are electric sparks, may be seen in the dark."
Aunt Mary's Tales, 1819
but I found this earlier description of a plant:
A General System of Nature, 1806
Well, according to Said What? the origin is derived from well-to-do families' homes.
If a maid cleaned the wood floor the wrong way, it would leave streaks in the floor, and the lady of the house would be annoyed or upset by this. Thus she was "rubbed the wrong way."