"If anyone would come after me"This refers to one who follows Jesus. It means to follow in Jesus' footsteps.
Jesus is God's loving servant. And he wanted us to follow him and also become the Supreme Being's loving servants.
"... he must deny himself ..."The phrase, "deny himself" is being translated from the Greek word, ἀπαρνέομαι (aparneomai) - which means, according to the 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 ones 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.
You see, the spiritual world contains no self-centeredness, only love among its residents. The only 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 decided not to love, naturally became self-centered due to the emptiness created by not loving others.
In other words, 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, it naturally turns upon ourselves.
Once we became self-centered, we fell out of the spiritual realm. We took on these temporary physical bodies, and became residents of the temporary physical world.
In this world we have no opportunity to see the spiritual realm and the Supreme Being with these physical instruments - the physical eyes and mind. This effectively satisfies our desire to get away from the Supreme Being and chase our self-centered dreams around.
Once we gain this physical body, we begin to collect things that we claim ownership over. This includes money, houses, cars and so on. But it also includes children, spouse, fans, members, etc. In other words, as we identify ourselves with this body, we begin to identify those people of our family and others that somehow are connected to our bodies such as those within the same country or religious sect - as belonging to us - or part of us.
This false sense of ownership creates the various wars between countries and religious groups throughout the world. As the various members of these groups consider their group as part of themselves - they fight to claim things for that group, seeing those things as extending to themselves.
But we really own nothing here. The Supreme Being owns everything. And all of these groups - whether they be families, countries or religious groups - are also temporary. Every physical body within the human population dies within a few decades - 100 years at most. And every country or religious group will also disband or change or assume a new name or otherwise fall away at some point in time.
So nothing here is permanent. And we cannot control any of it. We cannot even control how long our body will live, let alone others.
This means we are not the true owner of anything we might claim ownership of. We cannot control it, therefore we cannot be its owner.
Yet still we pretend we own these things. We still pretend that we will find happiness in these things.
This is what Jesus is speaking of. He is saying that if a person wants to become his follower, that person must give up this false sense of ownership and self-centered attempt to find happiness where there isn't.
"... and take up his cross and follow me."This is a mistranslation. Why would Jesus speak of the cross? Certainly when he spoke this he had not met with his crucifixion. It he suggesting that his followers all be crucified?
Don't be ridiculous. Furthermore, 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. The reality is that 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 grape vines, as well as fences and trees. 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 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 from their current place.
This is what Jesus is referring to. He is metaphorically stating that if anyone wants to follow him, he must not give up self-centeredness, and give up a life that is oriented around 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 began traveling to preach to others.
But does this mean that we have to leave our homes and our families? 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.
"For whoever wants to save his life will lose it, but whoever loses his life for me will find it."This 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.
(For a translation of Jesus' statements from the Book of Matthew without institutional sectarian influence, see the Gospels of Jesus - translated from the original Greek texts.)