Why do Christians value human life?

The single most direct answer to this question is that life has value because God created humanity in his image.

 "Then God said, “Let Us make man in Our image, according to Our likeness; and let them rule over the fish of the sea and over the birds of the sky and over the cattle and over all the earth, and over every creeping thing that creeps on the earth.” God created man in His own image, in the image of God He created him; male and female He created them." Genesis 1:26-27 

But, this is the easy question.  The harder question is, "What are the implication of being created in the image of God?"

1. People are different- Human beings occupy a distinctive and unique place in the created order. We are not just the smartest animals or the highest life form to have evolved as of yet and we not gods. We are the only things in the entire universe to be created in the image of God. It does not matter what that "image" actually is because what ever it is it sets humanity part. John Calvin said the end of our regeneration is " that we may be made like God, and that his glory may shine forth in us; and, on the other hand, what is the image of God…the rectitude and integrity of the whole soul, so that man reflects, like a mirror, the wisdom, righteousness, and goodness of God.” Even after the fall and eviction of Adam and Eve we still act as this kind of mirror.

2. Humans have intrinsic value- This ideas runs counter to our performance based culture that asks, "What can you do for me?" When your consumption becomes more than your contribution to the greater good or the collective you have over stayed your welcome and are no longer beneficial to the larger generating community. But if dignity and worth are not based in what you do or can produce and in the image of God implanted in each of us, our value is not commodity. Likewise, when our importance is not place in identifying characteristics or qualities (young or old, rich or poor, intelligent or simple, complete or missing part, male or female, black, yellow, white or brown, gay, straight married single), but on our personhood and humanity, we seek to move from extrinsic properties to an intrinsic ontology.

3. It provides us with a frame for interacting with each other- To devalue the imago dei in another person is to disparage the God whose image they carry. We are not to cheat, lie to, abuse or disrespect other people because they too carry the image of God in them.  An extreme cause of this can be found in Genesis 9:6. I think the imago dei also provides us with the basis for Jesus new ethic found in the Sermon on the Mount:
   
   

• If anyone slaps you on the right cheek, turn to them the other cheek also.
• And if anyone wants to sue you and take your shirt, hand over your coat as well.
• If anyone forces you to go one mile, go with them two miles.
• Give to the one who asks you, and do not turn away from the one who wants to borrow from you.
• “You have heard that it was said, ‘Love your neighbor and hate your enemy.’ But I tell you, love your enemies and pray for those who persecute you…

         Valuing human life then is a social ethic.

4. We are loved by God- The bible is replete with examples of God’s love for us. The most obvious is the coming of Christ, his death and resurrection.

• John 3:16 “For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life.
• Luke 19:10 “For the Son of Man has come to seek and to save that which was lost.”
• Romans 5:8 But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us.
• John 12:46 “I have come as Light into the world, so that everyone who believes in Me will not remain in darkness.
• Matthew 20:28 just as the Son of Man did not come to be served, but to serve, and to give His life a ransom for many.” 

What God in Christ did for us in the mist of our rejection and rebellion against him proves he loves us and sees us as valuable.  What a waste it would have been for Christ to die for something God thought was worthless.  If we are highly valued before the eyes of God, why would he go through so much trouble and pain to save us? This in turns models for us the value and worthy of all people, no matter if they are like you or not.