I agree that the conversation went downhill with both of you adamantly trying to prove that your way was right. This is hardly unusual when someone you care about tells you that you are wrong. Maybe when you have had some time to get over the hurt and betrayal of all this this, you can re-read the conversation and find a better way to approach telling those close to you. Many people will have very strong knee jerk responses, opinions and misconception of what poly truly is.
Maybe just start small. "This is what the wife and I decided to do, I'd like your support". If there is a negative response, "I'm sorry you feel that way, if it would make you feel better, please feel free to talk to my wife". Then change the subject and leave it at that. Don't engage in a debate yet.
Just an idea.