The exact incident could vary, but the scenario is the same. You are Project Manager / Program Manager of a team with colleagues who have different roles, and their emphasis at different parts of the schedule is different. At a particular point in the schedule, even though both Development, Usability and Testing are supposed to be on the same wavelength, their focus and push could be different, and that is very natural. In this particular case, the situation happened at the time of the schedule when we were supposed to stop all new feature work, from that point on, all the focus would be on resolving defects in the features already implemented.
This is a critical moment for the testing team, since they essentially consider this the time when the entire product comes together, with all features working to some degree or the other (one is really considering a development process that is not ideal scrum). The integration testing happens more critically from this point onwards, and it can take a lot of time from this point in the schedule to thrash through most of the defects and make the product stable (of course, you cannot find all the defects in the product). The testing team is expected to not welcome any addition of new features from this point onwards.
This was a critical time. Some of the members of the development team had come in mid-cycle, so there was already some instability in the team, and it did take them some time to understand the product code and understand the team dynamics and work together as a team. At this time, the Product Management came in with a critical new feature (that had been introduced by the competition) which was expected to take another 2 weeks to develop, with the remaining testing time being around 1.5 months. Now, this was not an easy situation. The testing team was well justified in terms of not agreeing to take this feature, since in the end, it was their responsibility to ensure that the product was stable and had the least number of defects possible. The product manager was quite serious in terms of the need for this feature, and was pushing for it. The development team was ready to implement it.
The first meeting to discuss this was a disaster, with these stated positions being discussed, and getting heated. For me, unfortunately, being the Program Manager, it was my responsibility to ensure that the discussion remained in reasonable limits of discussion, without getting heated, and nobody getting into an inflexible position. However, in this case, at some point, the discussion went into a thread of policy and schedules, and it turned out that I started taking a more inflexible position, whereby such a change would not be possible. The discussion terminated soon after, and it got escalated, and during the midst of a discussion with my manager, I realized my mistake (while I was being chewed out). In every discussion, typically the managers need to ensure that discussions need to remain on a civil level, discussions can get heated, but nobody should reach a point where they get into a position from there was no roll-back, and certainly not the Project Manager / Program Manager.