The thesis statement is a little problematic in that it is difficult to prove. Narrowing it a bit further may help, something like: "Anton Chigurh is a chilling symbol of the darker side of humanity" would be more simple. The thesis as written basically claims humanity is psychopathic, and while there are many examples of this in specific instances, I think placing all of humanity in that category might be hard to justify. Just a suggestion, of course.
Chigurh's character represents that absence of almost anything recognizably human, rather, he is merely an animal. He acts on instinct and reflex and he kills with neither emotion nor remorse. There are elements of humanity where this is the case, such as in war, where killing is not only encouraged, it is expected. Humanity's appetite for drugs, knowing full well the misery they cause at every step of the chain, the criminals they empower, the violence they engender, yet consumption remains high, and humans are quite cavalier in their attitudes towards usage.
You might also argue that Chigurh is a product of society. He wasn't born a psychopath, he was made one. He's been traveling 22 years and now he's here. He's the worst humanity can produce. The sum total of every vice and depravity. As readers, we are forced to acknowledge the dark side we don't want to admit each human has the capacity for.