John 8:13a 
So the Pharisees said to him, "You are bearing witness about yourself; your testimony is not true." 14Jesus answered, "Even if I do bear witness about myself, my testimony is true

Jesus does not appeal to a “higher authority” because there isn’t one! We think we can decide whether we accept Jesus authority or not but that’s not a decision we can make. We are under his authority because everything and everyone is! If we claim otherwise we are deluding ourselves. 

Accepting Jesus' authority sets us free because we are no longer relying on ourselves to work everything out. How am I supposed to be an expert on life when this is my first time through?! Isn't it much better to rely on the Author of life?