But why do people feel they are OK? What is the standard they are applying to themselves? Most people feel that if they are generally nice, tolerant and polite then they are fine. When they fail to meet even that standard if they have a good reason they still think they are fine. They think of themselves as social animals. Mostly self-absorbed but occasionally doing something out of empathy. Most of their relationships fill their own needs and are not really focused on the good of the other person. Sex is often a game rather than a gift. They don't feel particularly bad about any of that.
What evangelism needs to do is spark a desire for more. I say spark because the human heart naturally wants to burst into flame with this desire. We know we are meant for self-sacrificial love. We should have great courage and wisdom. There should be hope for an eternal rest in peace when we die. There should be profound truths about life that we can learn. We know we are meant to be saints. We just can't be satisfied with anything less. Evangelism is about awakening that knowledge in people's hearts.
When we do that then people will get that there is something deeply wrong with the way they are living their life. That hell is not just something Christians use to scare gullible people. Hell is just where this self-absorbed lifestyle leads. It logically should lead there. When St Paul calls people "senseless, faithless, heartless, ruthless" (Rom 1:31) they see themselves in that and get that that road has to lead to something bad.
So the good news of God's love for us and the bad news of our sin turn out to be 2 sides of the same coin. When we know we are meant to partake in the divine nature then our temptation to think of ourselves as animals is deeply offensive. Yet we still fall into it. That sends us to God begging for His grace.