"And the Lord's servant must not be quarrelsome but kind to everyone, able to teach, patiently enduring evil, correcting his opponents with gentleness. God may perhaps grant them repentance leading to a knowledge of the truth, and they may come to their senses and escape from the snare of the devil, after being captured by him to do his will." -Tim 2:24-26
"And the Lord said to Paul one night in a vision, “Do not be afraid, but go on speaking and do not be silent, for I am with you, and no one will attack you to harm you, for I have many in this city who are my people.” Act 18:9
"...brothers, pray for us, that the word of the Lord may speed ahead and be honored, as happened among you, and that we may be delivered from wicked and evil men. For not all have faith." 2 Thess 3:1
Let these Texts soak in deeply and remind us who is sovereign over the whole of creation and over the hearts of men ... For certain, it isn't me and it isn't you and it isn't those who hear the gospel. It is God and God alone.
These verses may change the whole way you look at evangelism. Instead of trying to simply argue others into the Kingdom, to believe on Jesus Christ, Paul clearly indicates that we are to patiently endure evil and falsehood when we encounter error, and we are to confront lies with gentleness. To correct people by just presenting God's word and that we are to pray. Why? Because we are to leave the actual changing of someone's heart to God. Our prayers for evangelistic success are to be for the word of God to be honored, to be believed. That is not something wicked men want, so we leave it to God to change their hearts. It is He who grants repentance That which is impossible to men and women (repentance and belief) is possible only with God (Luke 18:27). Only He can take the heart of stone and make it a heart of flesh (Ezek 36:26). When a heart is still stone it does not want to be softened because while it is still "stone" it signifies a heart that is stubbornly resistant against God ... but that is where God comes in ... to do something only He can do.
Consider this, why would Paul have the Thessalonians pray that the word of God speed ahead and be honored if he did not think God could, and would, actually do something to change people's hearts? If he merely wanted his readers to persuade their hearers of the truth of the Bible he could have asked them to better brush up on their logic and powers of persuasion. Of course these skills are also good to have, but ultimately it is God who uses the truth to make the difference. We can plant a seed, but a seed needs something more: the Holy Spirit, who alone can germinate that seed, and cause it to grow. Truth is, people's natural hearts resist even when presented with unassailable truth (John 3:19, 1 Cor 2:14, Rom 8:7). More data is not what they need to change their stubbornness, but a new heart. Frankly, we can preach till we are blue in the face but unless God works grace in the hearts of the hearers, there will be no change of direction. That is why Paul explains to the Thessalonians:
"For we know, brothers loved by God, that he has chosen you, because our gospel came to you not only in word, but also in power and in the Holy Spirit and with full conviction." 1 Thess 1:4-5
Peace be unto all who hear and may God bless His word, opening our eyes that we may behold wondrous things in His law (Ps 119:18)