Debate is the death of conversation.
Source, in full
In Lilless McPherson Shilling, Linda K. Fuller, Dictionary of Quotations in Communications (1997), p. 13. Most likely a variation of "Argument, again, is the death of conversation, if carried on in a spirit of hostility", William Hazlitt, Table Talk: Opinions on Books, Men, and Things (1846), p. 126