Let the other person explain his point of view by asking intelligent questions. In the end, who is able to understand better one's reasons is oneself; and people like this to be recognized.
Anger is other face of fear. Sometimes people get angry because their own motives, rather because of something with you.
Contra-argumentating so hardly many times is a clear indicator that the person recognizes the proposed solution is already good, but the person wants to get sure there isn't any drawback in taking it.
People tend to over-react on new changes, but this can easily be reverted by showing them how these changes already connect with their own objectives (not yours); and showcasing before getting into words.
What is visually measured tends to improve itself. Use the social tool-kit for actually being objective of what's really going on.
Evangelizing is more about informing than convincing, because convincing oneself takes time. With key information people tend to choose wisely what options actually makes things simpler.