Watch some of this video from the second 2012 presidential debate. Candy Crawley has to moderate (that is, lead) a debate between two people who are used to being the leader in their own worlds. Pay particular attention to the body language of Mitt Romney.
There is a key manipulation technique being used here by Romney and to a lesser extent by Obama. Notice how Romney walks forward toward Crawley as he tries to take over the conversation. That is a bullying technique. It is aggressively asserting power including a subtle threat of assault. Walking toward someone like this is a push for the other person to back down. And, as he gets closer, he makes himself appear both larger and higher in Crawley's vision as she is seated. This is another way of asserting power.
So, Crawley is put in an awkward position as the leader of the debate. She is being bullied by a presumptively powerful man. In most situations, he would expect to demand the leadership role in a room. But, Crawley is the leader in this situation, and she must retain the leadership in order to make the event successful. Part of the awkwardness comes because she can't rudely stand up and tell him to back off and follow the rules. But, she still needs to back him down. You can decide how good a job she did.
We find ourselves in these situations when we have to lead a meeting that includes managers above us in hierarchy. When I find myself in this situation, I emphasize the role I've been asked to play, and use the magic phrase "I need." It works wonders. "My role here is to keep us on track. I need to ask you to hold that thought for a few minutes." It's tough, but it's your role as the leader.