What does John 13:16 mean?

Peter's initial reaction to Jesus washing the disciples' feet shows how radical the act was (John 13:6–8). In the context of that culture, Peter assumed Jesus was denying His own role as Lord. Jesus has already clarified that this is not the case. In fact, He's strongly embracing His authority over these men (John 13:13). Jesus is not lowering His own authority, He is eliminating any excuse to shirk humility and service (John 13:14–15).

Here, Jesus continues to repeat this theme: servants are not "greater than" their masters. A person cannot point to something their Lord does and say, "I'm too important, too valuable, or too good for that." Washing of someone's feet, in that era, was among the clearest expressions of humility one could expect. Jesus leaves no room for doubt in interpreting His own actions: you are not above Me, so if I act humbly and in support of others, you have no right to refuse to do the same.

This incident overturns the natural human sense of leadership and community. Believers mutually submit, support, and care for one another. Godly leaders are servants, not snobs.