When team members are more personally invested in an issue you're most likely in People Problem Stage. In short, people are the problem here. Perhaps one your programmer works all night and is rarely seen during the day. Perhaps your lead assigned one background and the artist did six, many off the creative path of the project. Saving face and self-interest becomes important.
People sound emotional around the issue.
You hear put-downs and sarcasm. Management issues are more complex in this stage. It is very important that as a manager you do your best to get resolution. While you could avoid dealing with Day to Day Issues, it is death to your development project if you choose to ignore the People Problem Stage. As people want to be right and win, they can easily lose sight of the big picture.