“If anyone would come after me, he must deny himself ...” (Matthew 16:24-25)

“If anyone would come after me, he must deny himself and take up his cross and follow me. For whoever wants to save his life will lose it, but whoever loses his life for me will find it.” (Matthew 16:24-25)

What does he mean by 'come after me'?

This isn't referring to those who literally 'come after' Jesus. Is isn't describing someone who would chase after Jesus. Nor is he describing someone who would walk behind Jesus.

Jesus is referring to someone who would follow him: He is describing a follower of Jesus.

The phrase, "come after me," is being translated from the Greek phrase, ὀπίσω μου ἐλθεῖν. This means to follow or follow in someone's footsteps.

Jesus' life and teachings indicate that he is God's loving servant. And he taught that if we became a loving servant of God we would become fulfilled. Those who follow his teachings are followers.

How would a follower of Jesus 'deny himself'?

The phrase, "deny himself" is being translated from the Greek word, ἀπαρνέομαι (aparneomai) - which means, according to Thayer's lexicon, "to forget one's self, lose sight of one's self and one's own interests."

This means Jesus is speaking of the opposite of self-centeredness. Self-centeredness means to orient our focus and objectives in life around ourselves - or the supposed extensions of ourselves, the family of our physical body.

Self-centeredness, in fact, is the primary cause for the suffering that occurs within the physical world. All the bloodshed, greed and violence that occurs is a product of self-centeredness - those who consider their bodies or the bodies of their family and/or country or other organization of more importance than those of others.

In fact, the physical world itself is a product of self-centeredness. It is the reason we each are here in the physical world in the first place: Because we became self-centered.

The spiritual world is a place of God-centeredness. It is a place of love among its residents. The central goal is to please the Supreme Being and work for the welfare of the Supreme Being's children.

But because love also requires freedom, each of us has the choice to love or not. Those of us who have decided not to love became self-centered. This is created by the emptiness of not loving others.

We all need to love and care for someone. It is our nature. But if our love is not directed to the Supreme Being and His children, that creates a hole, or emptiness. 

Such an emptiness creates self-centeredness. This is how we fall out of the spiritual realm and take on these temporary physical bodies. We become residents of the temporary physical world to exercise our self-centeredness, and to learn lessons of love.

In this world, we have no opportunity to see the spiritual realm and the Supreme Being with the physical eyes and mind. This effectively satisfies our desire to be away from the Supreme Being and chase our concepts of self-centered happiness.

What does 'take up his cross and follow me' mean?

This is a mistranslation. Why would Jesus speak of the cross? Certainly, when he spoke this he had not met with his crucifixion. Is he suggesting that his followers all be crucified?

Don't be ridiculous. Jesus did not even carry his own cross. A fellow named Simon of Cyrene was forced to carry the cross that Jesus was crucified with according to Mark 15:21. 

Jesus is not speaking of his or anyone else's cross here.

The word "cross" is being translated from the Greek word σταυρός (stauros), which can mean a cross, but also means, according to the lexicon, "an upright "stake", esp. a pointed one, used as such in fences or palisades."

The most common use for the "stake" was to prop up grapevines, as well as fences and trees. These stakes were also removable and could be moved to different vines or trees as needed.

In fact, we still maintain the expression that refers to what Jesus is talking about:
"pulling up stakes"
To "pull up stakes" is a metaphor that refers to a person leaving a particular plot or field, or their current home or land. It comes from the time when farmers or landowners would take the stakes they had used to prop up their vines, trees, and fences with them and move. Or they could move them to a different field of vines.

This is what Jesus is referring to. He is metaphorically stating that if anyone wants to follow him, he must be prepared to give up a life of self-centeredness. This means "pulling up stakes" from the various concerns and objectives we have and redirecting our lives towards coming to know, love, and serve the Supreme Being.

This is certainly what Jesus did. He left his home and he began traveling to preach to others.

Does this mean that we have to leave our homes and our families in order to follow Jesus? Not necessarily. Jesus is asking that we give up the notion that they are our real homes; and our sense that they belong to us; and our thinking that they will fulfill us.

What does 'whoever wants to save his life will lose it, but whoever loses his life for me will find it' mean?

"Loses his life" is not referring to our physical body. It does not refer to the body being killed or murdered or committing suicide. Jesus is speaking of leaving behind a life of self-centeredness.

Currently, our lives are absorbed by ourselves. We are always thinking of our own welfare. The status of our physical well-being, what others think of us, how wealthy or powerful we are. This is the consciousness that Jesus wants us to depart from.

Leaving that consciousness behind means putting the Supreme Being first in our lives. Leaving behind our self-centeredness for Jesus means putting God first in our lives. This is to follow Jesus.

God-centeredness is the key to happiness. Those who seek self-centered happiness never find it. Rather, one who leaves behind self-centeredness and seeks to come to know, love, and serve the Supreme Being and His children will find happiness even though he is not seeking it.