In John 15:16, Jesus tell us that He chose us to bear fruit that remains. In light of what He commands in Matthew 28:18 – 20 and His prayer in John 17, at least part of that expectation of fruit is in leading others to follow Him.
You might ask, “How does sharing the gospel with others draw you closer to Christ?” Great question. In his book Dedication And Leadership, Douglas Hyde, who converted to Catholicism from being the head of the communist party in Britain, compared the training of Christ to the training methods of the communist party. He found several interesting parallels. One that is particularly interesting is the early engagement of the new disciples in spreading the message of the movement. He relates that at his first party meeting he was given a stack of party newspapers and was instructed to go out on the streets and sell them and not to return until he had distributed them all. You might say that was a stretching experience for him. He was hit with a tsunami of questions for which he neither had answers nor even categories. When he returned to the meeting he was full of questions, a sponge for any information that he could use, and systems by which he could catalog and retrieve that information for use.
That has been my experience in sharing the Gospel as well. As the Lord has given me opportunity, I have shared the faith. Each person has questions that are different. I have not been able to answer them all but the questions have driven me back to the Lord in prayer, the Word, and in the community for those who have encountered similar objections. I have seen people who seemed hopeless, transformed by the power of the gospel. I have been transformed by the experience.