It's a question not often asked. The belief in eternal life is at the heart of the Christian faith, but why does God give the gift of eternity? If everything God does is purposeful, then obviously everlasting life is granted for a reason? It's not a "just because" kind of act.
Of course, one could quote John 3:16 at this point-- "‘For God so loved the world that he gave his only Son, so that everyone who believes in him may not perish but may have eternal life." So, God offers us eternity because of God's love for us. That's a great place to start, but let's probe a little deeper.
All of us who have experienced the death of someone we have loved, knows that the pain of death is the separation from that person, the end of that relationship in this life. We do not want the relationship with those whom we love to end. Why is that? Could it be that our desire for our relationships to continue reflects the character of the relational God who created us? If we accept the belief that there is a Creator and that Creator is relational and loving, then it is logically coherent to accept that human life does not end at the cessation of biological functions. There is more to come. In other words, just as we want to love our loved ones for all eternity, so God wants to love us forever as well. God no more wants his relationship with creation to end than we do. God will not coerce us into that eternal relationship. God makes the offer to us in Jesus Christ and we have to receive that offer in faith. But we must know that for God not to grant the possibility of eternity to creation-- content only to be in relationship with us for only the handful of decades we live in this present earthly existence-- is ultimately not a full act of love. If God only loves us only for this existence moving on to the next generation and the generation after that, we would rightly see our deity as a love 'em and leave 'em kind of God. We must heed the words of the Westminster Shorter Catechism, "The chief end of humanity is to love God and enjoy God forever." Our end is eternity in relationship with God.
But there is another reason, God grants eternal life to creation. God is not only a God of perfect love, but God is perfectly just as well. If God is just, God must at some point make all things right. Here I am relying on the work of Anglican priest and physicist, John Polkinghorne. If everything is to be put to rights, it cannot happen in this current futile state. There can be no fully attainable utopia this side of human history. This does not mean that human beings should not be diligent in seeking justice and peace for all, but a terrestrial utopian kingdom cannot be utopian simply because "it could only be the subject of the transient enjoyment of its mortal members, and it would have been denied totally to all the generations that had preceded its coming" (Science and the Trinity: The Christian Encounter with Reality, p. 149). Those preceding generations cannot find such justice unless there is a destiny beyond their deaths.
Justice can only be achieved if there is life after death. Polkinghorne writes eloquently on the matter. "We shall all die with our lives incomplete, with possibilities unfulfilled and with hurts unhealed. This will be true even of those fortunate enough to die peacefully in honoured old age. How much more must it be true of those who die prematurely and painfully, through disease, famine, war or neglect. If God is the Father of our Lord Jesus Christ, all the generations of oppressed and exploited people must have the prospect of life beyond death, in which they will receive what was unjustly denied them in this life" (p. 150). If there is no eternity, the dead children of Syria, Honduras, and Afghanistan will never receive the justice denied them in this life.
Every human being has experienced life's incompleteness. We not only sense this with our own lives, but with the lives of our loved ones and friends. We may enjoy the blessing of parents who lived to a ripe old age, but after death, there is still more we would like to say if we could, and there is still more we wish we could do with them. Their absence at the table is felt, years after their demise. It is because we human beings are relational and loving that we feel this sense of incompleteness. If God is loving and relational as well, God too does not want the relationship with his Creation to end. God desires more as well.
If God is just, then everything must be put to rights. If there will be no ultimate justice given to the victims of the Holocaust and served to its perpetrators, then if there is a Creator, he is neither loving nor just. That God is not a subject worthy of our worship.
Atheism is to be preferred to the belief in an unloving, uncaring deity who is content to let creation fade out of existence.
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I do not seek to understand that I may believe, but I believe in order to understand. For this also I believe, –that unless I believed, I should not understand.-- St. Anselm of Canterbury (1033-1109)