Be Gentle. Be Patient. Be Meek.
STOP wasting time getting upset and stressed out at the way lost people react to you when presented with the truth of the gospel.
Born again Christians should expect sinners to be confrontational. I was, when first confronted with the gospel.
Additionally, expect sinners to act irrational and to say things that don't make sense biblically. That's what lost people do. That's why the Bible calls them "lost" and it's exactly why Christ came.
Luke 19:10 For the Son of man is come to seek and to save that which was lost.
Instead of stressing and getting upset at those who reject truth, follow the instructions found in the Bible. God's word has a simple and effective solution for handling these types of situations: be gentle, be patient and be meek!
2 Timothy 2:24-26 And the servant of the Lord must not strive; but be gentle unto all men, apt to teach, patient, In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth; And that they may recover themselves out of the snare of the devil, who are taken captive by him at his will.
Remember, sinners are NOT opposing you, they are opposing themselves. So, relax, breathe and don't take it personally. Instead, pray God will give them repentance.