Short answer – sin. Sin is what is wrong with people. It is a universal malady. In an essay entitled “Justification in Galatians,” Douglas J. Moo quotes Stephen Westerholm: “The fundamental question addressed by Galatians is not ‘What is wrong with Judaism (or the Sinaitic law)?’ but ‘What is wrong with humanity that Judaism (and the Sinaitic law) cannot remedy?’” Later in the essay, Moo states, “Works are a problem in Galatians, therefore, not simply because they involve an outmoded torah; they are a problem also, and more fundamentally, because human inability renders them incapable of delivering people from sin.” As someone poetically stated, the heart of the human problem is the problem of the human heart.
The reason that obedience to the law of God won’t work as a way of salvation is that no human being is capable of conforming to the law of God. None of us can obey it. We fail miserably. Like a mirror, the law can show us our true condition as violators but it cannot save us. Like an MRI, it can reveal the disease but it can’t heal it. This is why Paul insists that no flesh will be justified by the works of the law (Gal. 2:15-16).
People cannot fix what’s wrong with people. Only God can do that. He sent Jesus Christ to become a curse for us so that we could be delivered from the curse of the law (Gal. 3:10-14). Dying on the cross and bearing our sin, Jesus was cursed so that we could be redeemed. Those who trust in Jesus Christ are counted righteous by God (Gal. 3:5-9). Jesus was treated like a sinner so that those who trust in him could be treated as righteous.