I have to say, I feel for your wife on this one... I really hate when people speak to me using "methods" (e.g. "I hear your anger."). I just want to hear someone's genuine thoughts, particularly if we're in an argument. I don't want them to be trying to manage my reactions.
That said, it sounds like you were really trying to do the best thing. It sounds like as well as having a calmer discussion about whatever the argument topic was, you also need to discuss your communication styles. She needs to explain what was so off-putting about your approach; and you need to explain what you were trying to avoid by not speaking spontaneously.