One of the skills we seem to have lost as a society is the ability to have conversations with people with whom we disagree and trying to change their minds. More often these days, the trend is to (literally or metaphorically) stomp off in a tantrum and stop talking to them. You see many people now demanding that those who disagree with them "unfriend" them on Facebook.
Richard Dawkins has always been a role model in terms of communication, having written some of the most influential popular science books of the twentieth century, including The Selfish Gene and The Blind Watchmaker.) Here is his advice:
As a magician, persuasion is part of the toolkit. I need to convince people that a specially prepared prop is ordinary, or that there is no way I could possibly know a piece of information I, in fact, already do. The heat and soul of it is:
The important, and often overlooked, point is sympathetically. You can't assume (as many people seem to now) that the reason that people don't see things your way is because they are just morons. Whether you articulate it that way or just think it, it doesn't put you in a good position to begin changing their mind.