Over the years I've found that a key concept I must rest in as I talk to others about Christ if I'm to avoid despair, hopelessness, and even anger is this: My job in evangelism is to focus on presenting and clarifying the gospel and its implications, not to convert people.
Though a person's salvation is initiated by God ("No one can come to Me unless the Father who sent Me draws him," John 6:44) and completed by God ("These whom He called, He also justified; and these whom He justified, He also glorified," Romans 8:30), our communication to others is (usually) the instrument God chooses to work through to bring others to Himself. We speak the message to others, and He will either choose to move them at that time or He will not. We need not be anxious about "sealing the deal" in our encounters with non-Christians because their conversions are not our responsibility.
So what is our responsibility? J.I. Packer, in his book, Evangelism & the Sovereignty of God, talks about our biblical mandate to tell others the good news about Christ:
We are all under orders to devote ourselves to spreading the good news, and to use all our ingenuity and enterprise to bring it to the notice of the whole world.... While we must always remember that it is our responsibility to proclaim salvation, we must never forget that it is God who saves.... Our evangelistic work is the instrument that He uses for this purpose, but the power that saves is not in the instrument.... (pp. 26-27)
If only the communication of the gospel is our responsibility, we will take a tremendous amount of pressure off ourselves if we focus on clarity rather than conversion. Speaking to those who are likely to be reading this blog, all of the apologetics we learn—whether theology, historical facts, tactical/analytical skills, or philosophy—are for the purpose of explaining clearly the truth about God in a way that truly communicates the message to the listener and honors and glorifies God by displaying His truth as literal truth about reality to the world.
But our task as a body of Christians is not accomplished only through apologetics; those who are gifted in apologetics speak the truth about God in those terms, and those who have gifts of mercy or hospitality display the truth of God's character in these ways in addition to their verbal proclamation of the message. Using our various gifts to clearly communicate the truth fulfills our responsibility as God's messengers whether or not He chooses to move in the listener's heart at that time.
Once I grasped this concept and focused on clarifying the gospel, answering questions and challenges in a way that honored God's truth, and leaving conversions to the Holy Spirit, my conversations immediately lost much of their pressure and stress.
[I]f we forget that it is God's prerogative to give results when the gospel is preached, we shall start to think that it is our responsibility to secure them. (p. 27)
Taking on a responsibility we can't possibly shoulder is what will lead to despair. We must simply remember that our success is not determined by conversions, but by our faithfulness and dependence on Him as we continue to fulfill the task He's given us to act as His ready instruments of communication, never knowing when He will choose to remove the brick wall from behind a friend's eyes.