Q: "Why do Christians refer to other people as 'lost'? That seems so condescending, so arrogant!"
our A: It was Jesus who first used that term. Jesus said that the reason he came was "to seek and save the lost."1
Then in the mid-1700s, John Newton (a former slave trader), wrote the famous hymn, "Amazing Grace." The first few lines read: "Amazing grace! (how sweet the sound) that saved a wretch like me! I once was lost, but now am found; was blind, but now I see." Many followers of Jesus personally relate to that, as a good description of their own life.
It is certainly ok for Jesus to use the term "lost." His motives are clearly humble, sacrificial and compassionate, "to seek and save the lost." Also, any person has the right to say, about their own life, that they were once lost. The rub comes when it's said about someone else.
Why would Jesus describe people as lost? Mainly because they were relying on religion. They were sure that their diligence in following religious ceremonies, religious laws and restrictions made them acceptable to God. They were confident in their proud, self-righteousness. But Jesus said their hearts were far from God. They had a relationship with religion, but not with him.
On many occasions, Jesus openly challenged the religious leaders about pointing others toward these strict religious rules, rather than toward God.
Jesus invited them, "Come to me, all who labor and are heavy laden, and I will give you rest. Take my yoke upon you, and learn from me, for I am gentle and lowly in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light."2
What was keeping them from God was their sin, and no amount of self-effort or religious devotion would take care of that. They needed God. Out of great love for us, Jesus took all of our sin on himself on the cross, to gain our complete forgiveness. It is why we can freely come to God. No dedication to religion required. No pressure to try to earn God's acceptance, to post a good image. In a real way, as we are, he invites to know him, to no longer be without him.
To see more on Jesus' life and how you can know God in a personal way, please see Beyond Blind Faith.
(1) Luke 19:10
(2) Matthew 11:28-30