You're right, up to a point; God has placed within each of us a sense of right and wrong (what we usually call our conscience), and it certainly should lead us to do what's right. This is why the Apostle Paul could say to those who falsely accused him of wrongdoing, "I have fulfilled my duty to God in all good conscience to this day" (Acts 23:1).
The problem, however, is that our consciences have been dulled by sin -- and the more we sin, the duller they become. In fact, our consciences can become so dulled by sin that we no longer want to do what's right, and may even lose sight of what's right and wrong. Our moral sense becomes twisted, and we end up calling evil what is good, and calling good what is evil. The Bible condemns "the godlessness and wickedness of people, who suppress the truth by their wickedness" (Romans 1:18).
Don't be surprised at what is happening around us today; our world is largely in rebellion against God. In addition, behind the scenes Satan is also at work, doing all he can to deceive us and turn us against God.
But don't be discouraged either. God is also at work, and someday the victory will be His, when Christ returns to establish His Kingdom. In the meantime, make Christ the center and foundation of your life, and make it your goal to live each day for His glory.