Sometimes it's better to let someone else take the lead and shine.
Say if you are a team lead based on seniority alone. Imagine you and your team are given a task to perform that you have no experience with that particular area. Do take the lead and totally screw up the job just because you were the designated leader and there was pride on the line? Times like this call for backing off and giving the lead to perhaps a team member with less seniority but with more experience.
The advantages outweigh seniority and pride as the job has a better chance of being done right with the right leader. It gives them a sense of pride and experience as a leader that can be used later on. You are also not under the usual pressure to perform but to support. In sitting in a supportive position you can evaluate your team member in a new role and the other team members reaction to him or her. You are still a part of the team and can be there to answer any questions the team members have in that situation.
It's definitely a win-win scenario. You get a break and another person gains valuable experience in a new role. Every one involved learns something new.