The dystopian near-future of the film is a result of our attempt to cure ourselves (of cancer)—instead this unleashed a virus that killed most, turning nearly all of the remaining population into near-mindless cannibals unable to survive in the light. Ravaged by disease, misshapen, out of their minds, they savagely attack and devour anything showing signs of true life. The protagonist, Robert Neville, believes himself to be the sole survivor. A scientist and military man (great combination if you're going to be the last man on Earth), he is driven to find a cure for the condition of the infected populace (work he'd begun before the cataclysm).
Cornered behind plexiglass cracking under the onslaught of sub-humans with snapping jaws, Neville discovers that, after years of trials and failures, he has a cure that will work. Desperately, he cries out, "I can help! I can fix this! Let me save you!" Too far gone, the sub-humans continue their attack, bent on destroying the one man who can save them. Their fall is both horrific and tragic.
The offer of salvation from the One who can give it is likewise often met with snapping jaws and violence. Though we know we are broken and diseased, we want our own way, lashing out at life and light. We create our own "order," rejecting health and hope, except as something to devour and destroy for our own ends. We are so much less than we are created to be, and it seems we're committed to making every effort to keep it that way. Because we no longer possess the capacity to imagine anything better than our own desire, our rage often becomes focused on the One who offers salvation.
One of the wonders of the gospel is that even this was part of His plan—He knew we would destroy Him, and He made our violence an integral part of His mercy. That's a kind of hope and grace I cannot fathom, much less undo.