As much as it would be ideal to calmly, politely and rationally explain your position, have the other road user listen to you and acknowledge they might have been at fault and apologise, followed by all parties going on their way, carefully, attentively and considerately using the road for the remainder of their journeys, happy with the amicable outcome, it doesn't usually work like that.
Torrents of abuse and shifting the blame onto the victim through some daft non sequitur are the more common outcome, indeed sometimes also from others who were not involved (like in Biggsy's case). I'm not suggesting that you always get the best results from going nuclear straight away, but that sometimes being polite and calm ends up in you getting walked all over.
If you've ever had a really close call, it's hard not to take it personally. You have my sympathies, Biggsy. Driving is a responsibility that most people don't take seriously enough.