Question: "What is the bad news / good news approach to sharing the gospel?"
Answer: Everything in life has good news and bad news associated with it. The entire truth is generally found in a combination of both. Emphasizing one side to the exclusion of the other is not the whole truth. The same is true of the gospel of Jesus Christ.
The bad news, spiritually speaking, is that we are all sinners deserving of hell for our sin against a holy God (Romans 3:23; 6:23). Our sin has kept us from His presence and eternal life (John 3:15–18). No one can earn his or her way into the presence of God because there is “no one righteous” (Romans 3:10). Our best human efforts to please God are “as filthy rags” (Isaiah 64:6). Some evangelists and street preachers focus exclusively on this aspect of God’s truth, which could be considered the “bad news approach.”
The good news is that God loves us (John 3:15–18). He wants a relationship with His human creation and has communicated with us in a variety of ways such as nature (Romans 1:20), the Bible (2 Timothy 3:16), and Jesus coming in human form to live among us (John 1:14). God does love us. He does want to bless us. He wants a relationship with us and desires to teach us His ways so that we can become all He created us to be (Romans 8:29). Teachers who focus only on the good news are leaving out a vital part of God’s plan of salvation, which includes repentance (Matthew 3:2; Mark 6:12) and taking up our cross to follow Jesus (Luke 9:23).
Until we know the bad news, we can’t truly appreciate the good news. You would not appreciate a stranger bursting into your home and dragging you outside, unless you first understood that your house was on fire. Until we understand that we are destined for hell because of our sin, we cannot appreciate all that Jesus did for us on the cross (2 Corinthians 5:21). If we don’t realize how hopeless we are, we won’t recognize the great hope Jesus offers (Hebrews 6:19). Unless we recognize that we are sinners, we can’t appreciate a Savior.
The best approach is to present what the apostle Paul called the “whole counsel of God” (Acts 20:27). God’s whole counsel includes both the bad news about our natural state and the good news about God’s plan to redeem us. Jesus never eliminated either of these when He brought “peace on earth, goodwill toward men” (Luke 2:14). His peace is available to everyone who is brought to repentance by the “bad news” and joyfully accepts the “good news” that He is Lord of all (Romans 10:8–9).