I do not think, sir, you have any right to command me, merely because you are older than I, or because you have seen more of the world than I have; your claim to superiority depends on the use you have made of your time and experience.

This quote is saying that being older or having experienced more does not mean someone has a right to tell someone else what to do. It is saying that a person’s superiority is based on what they have done with the time and experiences they have had. It is pointing out that age and experience alone are not enough to make someone better than someone else.