Announcing any kind of surprise or unwelcome news can be problematic in a group situation. When people have an emotional response, they want to express it, and in a group situation the mutual reinforcement can quickly scale up the emotion.
This is why it's generally not a good idea to quit by standing up in a staff meeting and announcing it to everyone at once (unless you're trying to make a scene :-)). It's much smoother to tell your boss first, so that they can help manage the emotion of the team.