What does Matthew 16:25 mean?

The idea that following Jesus shared anything with crucifixion—the tortuous, humiliating, violating death on a cross—would have shocked the disciples. Still, He has said anyone who would follow Him must deny himself and take up his cross (Matthew 16:24). Jesus had not yet revealed that He would die on a cross, though He will include that later in His teaching (John 12:32–34). Instead, He presented this as the most vivid of metaphors. Those who followed Him would have to willingly die to every bit of their own agenda, their own identity, their own approach.

Now Jesus becomes even more clear that He is describing the death of self: whoever would save his or her life will lose it. However, those who willingly lose their lives for His sake will find true life. In saying this, Jesus changed the stakes. Death to self is required to follow Him, yes, but it is also required to find the life that is truly life. In other words, Jesus says that following Him comes at the terrible cost of losing oneself, but the alternative is to permanently lose one's life.

Jesus will make clear in the following verses that this loss of life for those who do not take the hard path of following Him will come at the judgment by Jesus and His angels (Matthew 16:27).