The way I always understood this is that sin is reprehensible to a holy God, so therefore remaining in sin results in death. And by death I mean real, honest-to-goodness death, as in annihilation, not an eternity spent roasting like a weiner (I realize this is not the mainstream, orthodox Christian view, but I have a rather weird and eclectic religious background :>). That death or annihilation is not so much a punishment as it is just a natural outcome of things. It's sort of like someone falling from a ship into the ocean. If they are not rescued, they will eventually die, because humans are not adapted for long-term survival in the ocean. Neither God or the ocean are "punishing" the overboard individual: nature is just taking its inevitable course. We are all born in that ocean and need to be rescued. The Bible says that the wages of sin is death (Romans 6:23). Wages are what you get for what you do. God does not want anyone to collect those wages (Second Peter 3:9). His gift is eternal life (Romans 6:23 again).
In an ultimate act of love, God decided to throw a lifeline to a humanity which was and is drowning in an ocean of sin. He did so by actually dying himself in the form of Jesus Christ, thereby paying the penalty for our sins. Some object that Jesus did not stay dead, and therefore merely suffered a weekend inconvenience before being resurrected. But his resurrection was also part of overcoming sin: an overcoming that benefits us all and allows us to be rescued.
In the face of all this, God asks us if we want to be rescued. The rational answer would be of course we want to be rescued: we're drowning and our lives are at stake. But humans are not rational by nature. Sin and all the attitudes, emotions, and behaviors that support it limit our rationality. Lack of faith is also a major impediment. Christianity is largely a matter of giving faith a chance. It takes a good deal of introspection to realize that we need to be rescued.
If we decide to be rescued, then obviously we are doing so initially to save our skins, and God wants us to do that, because he is not willing that any should perish. But as our Christian faith develops, our motivation should change so that we obey God out of love rather than out of a fear of death and desperation for survival. First Corinthians 13 shows that love should be our motivation in all we do. If we don't obey God out of love, then our faith and any works we do are meaningless. A relationship with God cannot be based on fear. It can and should be based on respect, and sometimes that is mistaken for fear, but the sort of fear engendered by a horror movie should never be the basis our relationship with God.
As the preacher said, "I could write shorter sermons, but once I get started I get too lazy to stop." (A quote by Abe from the movie "Lincoln" [ 2012]). :>)
