Perhaps your friend isn't as sensitive as he should be—but have you ever asked yourself why he is acting this way? Is it simply because he wants to convince you he is right and you are wrong—or is it something deeper?
The reason, I suspect, is twofold. First, I suspect that now that he has become a Christian, his life has been changed. No, he hasn't become perfect—but down inside he knows God has forgiven him, and he no longer feels guilty over the things he did wrong. He also knows God has come to live within him by His Spirit, and he now has a new purpose in life. The Bible says, "Therefore, if anyone is in Christ, he is a new creation; the old has gone, the new has come!" (2 Corinthians 5:17).
Second, I suspect he really cares about you—and he knows your life would be much different if you came to know Christ also. In other words, he wants you to experience what he has experienced, and he also wants to know that you will go to heaven when you die. He knows you are on a dead-end road, whether you realize it or not—just as he was.
Don't turn your back on what God is saying to you. The Bible says, "Now is the time of God's favor, now is the day of salvation" (2 Corinthians 6:2). Open your heart to Christ today.