The principle that it is rude to interrupt another speaker goes back at least to Cicero, writing in 44BC, who said that good conversation required “alternation” among participants… The rules we learn from Cicero are these: speak clearly; speak easily but not too much, especially when others want their turn; do not interrupt; be courteous; deal seriously with serious matters and gracefully with lighter ones; never criticise people behind their backs; stick to subjects of general interest; do not talk about yourself; and, above all, never lose your temper.
Probably only two cardinal rules were lacking from Cicero’s list: remember people’s names, and be a good listener. Each of these pieces of advice also has a long pedigree. At a pinch you might trace the point about names back to Plato. Both found a persuasive modern advocate in Dale Carnegie, a teacher of public speaking who decided in 1936 that Americans needed educating more broadly in “the fine art of getting along”. His book “How to Win Friends and Influence People” is still in print 70 years later and has sold 15m copies. To remember names, and to listen well, are two of Carnegie’s “six ways to make people like you”. The others are to become genuinely interested in other people; smile; talk in terms of the other person’s interests; and make the other person feel important.
They then cite some interesting findings in "politeness theory":
The Brown and Levinson model says, roughly speaking, that Person A probably does not want to be rude to Person B, but in the way of things, life may sometimes require Person A to contradict or intrude on Person B, and when that happens, Person A has a range of “politeness strategies” to draw on. There are four main possibilities, given in ascending order of politeness. The first is a “bald, on-record” approach: “I’m going to shut the window.” The second is positive politeness, or a show of respect: “I’m going to shut the window, is that OK?” The third is negative politeness, which presumes that the request will be an intrusion or an inconvenience: “I’m sorry to disturb you, but I want to shut the window.” The fourth is an indirect strategy which does not insist on a course of action at all: “Gosh, it’s cold in here.” The first three of those options are plain instrumental speech, and are the sort of approaches that the conversation manuals warn you against. The fourth one alone leads into the realm of conversation as such. Here the purpose of speaking is not so much to get a point across, more to find out what others think about it. This principle of co-operation is one of the things that sets conversation apart from other superficially similar activities such as lectures, debates, arguments and meetings.