Read The Selfish Gene by Richard Dawkins. If you think about this question from the standpoint of a gene which is trying to propagate itself, it all makes sense.
Briefly:
1. think of human organisms as giant complex machines containing genes, whose purpose is to propagate the existance of those genes.
2. age of reproduction is roughly 16-40.. Genes which contribute to a healthy organism reaching this age and reproducing are selected to continue, and will become widespread in the gene pool.
3. From an evolutionary standpoint, past 40 and there is less benefit, so genes that extend life are not strongly selected. Although there is some benefit to being a grandparent to one's genes (if you are around you can help your grandchildren, who contain 1/4 of your genes), which is probably why our lifespan doesn't end right after the fertility years.
4. Your urge to live forever is simply an expression of the survival instinct. We are genetically programmed to want to live with every fiber of our being, and to do nearly anything to survive. If we weren't that way (say we had a weaker survival gene), we'd be more likely to die, less likely to propagate our genes, hence they would gradually vanish from the gene pool; leaving only 'strong survival' genes.
