Never the twain shall meet
Two things which are so different as to have no opportunity to unite.
Twain derives from the Old English twegen, meaning two. The phrase never the twain shall meet was used by Rudyard Kipling, in his Barrack-room ballads, 1892:
"Oh, East is East, and West is West, and never the twain shall meet."
There, Kipling is lamenting the gulf of understanding between the British and the inhabitants of the Indian subcontinent. It may well be that he coined the phrase - at least, I can't find an earlier citation of it in print.