You’re right; Christians do want to make the world a better place — and also point people to the better world God has prepared for us in heaven. You’re also right when you say that it doesn’t seem logical for people to hate and even kill them.
And yet, from the beginning, that’s exactly what happened. Jesus came into the world announcing good news, but His enemies put Him to death. For centuries Christians were often persecuted by the Roman authorities, and since then untold numbers have died for their faith in Jesus. This did not only happen centuries ago. During my lifetime, millions have been persecuted or killed for their faith by hostile authorities.
Why is this? The reason can be summed up in one word: sin. The human race has rebelled against God, and instead of wanting to seek God and live by His truth, we resist God and want to go our own way. Instead of loving God as we should, we hate Him — and we also hate His people. Jesus warned, “A servant is not greater than his master. If they persecuted me, they will persecute you also” (John 15:20).
When we give our lives to Christ, however, our hearts are changed. God Himself comes to live within us, and by His Spirit He gives us a new love — love for God, and love for others. Pray for those who face persecution today (sometimes in subtle ways) — and pray that you will be faithful to Christ no matter what you might face in the future.