Paul's statement in verse 19 shows a description of Christ. He was free from everyone and did not have to make the sacrifices that he did to redeem mankind, but he made himself servant unto each of us. The Savior's act of the atonement shows one of His characteristics-absolute selflessness. Throughout His life, Christ did not think of Himself, but always about those who were around Him. Even after He suffered in the Garden of Gethsemane and again on the cross, He thought about helping others when He healed one of His captor's ears and then forgave those who put Him on the cross.
This selflessness is an attribute of Christ that is being fought against today. Today's world is all about doing what is best for you. The world says that you are "free from all men", so why would you bind yourself down? Why would you get married and raise a family, why would you try taking time out of your busy day to help others, or spend time and money taking care of your elderly parents when you are free? Why would you choose to do anything other than roam the world and live your dreams without any other cares? But the world's message is in direct opposition to what Christ's message is, who "made [himself] a servant unto all."
At the end of his statement, Paul says that "I made myself a servant unto all, that I might gain the more." How could you gain more when you are serving others? This question goes back to the age old question, how do you gain happiness? I think you can gain more happiness by giving part of your life to others, whether it is through service or through developing meaningful relationships that might make you less free in terms of the world. The happiness that can come from these things can make you more free than you could be by following what the world says will give you freedom.
Just remember in life not to spend too much time on the things that aren't going to last (even if they seem as if they will bring you more freedom) that you miss out on the things that do last and can bring much joy into your life.
For more on this subject, here's a talk that is somewhat related, especially the first portion about spending time with those that we love.





