If you've read the Illiad, you'll get where I'm coming from on this:

The immortal gods have all the time in the world to be petty; humans have all the time to lose their chance to change the world.

How quickly would life become meaningless? How quickly would we tire of our endless youth? If everyone lives forever, then what is there to live for? Human beauty comes in the brevity of our lives, and from our ambition to change the world in this tiny time slot. We are all dying, dying every day. Most people become aware of this even as children, and it makes everything we do so much more important- because we DON'T have forever to do it in. When you're living under a time limit you have so much more to live for.

Immortality would devalue human life, I think.