The great Evangelist George Whitefield has revealed that true conversion is twofold - it's not just a repentance of one's sinfulness but also a repentance of the sin of self-righteousness. There is no other way to turn from sin but to repent or change one's mind about it, which begets a change in purpose. Biblical repentance is a repentance of one's sins and sinfulness. Part of the whole repentance of sin process is to repent of one's pride of life which includes self-righteousness.
Real repentance does not stop with repenting of the obvious sin but also of one's self-righteousness. To hide behind our own good works is useless because as Romans 1:10-19 and James 2:10-11 says, all men are guilty before God. A person does not need to commit such a huge sin to go to Hell, one just has to reject Jesus to go to Hell. Nobody needs to be as wicked as the most wicked person alive, all it takes is just one sin to fall short of God's glory. There is no such thing as as long as I do more good than bad then I am okay because it only takes one sin to fall short of God's perfect standard.
I have noticed how self-righteous people are indeed angry with the Gospel preachers unable to accept their own sinfulness. John 3:20 warns that the doers of iniquity hate the light lest their evil be exposed. Have you ever observed how a self-righteous person reacts when they are rebuked? Do not expect them to be appreciative but be ready to see them explode. A lot of self-righteous people think nothing is wrong with them even if their lifestyles say otherwise that they are not okay with God. What is worse you may encounter people who belief that they can save themselves by their works while they are living life like they have a license to sin.
Any true Gospel preacher would not just talk about obvious wrongdoings but also the sin of self-righteousness. To teach a gospel of works is just as dangerous as to teach a gospel that allows one to sin all they please. Galatians 3:24 declares that the Law is the schoolmaster that shows us our sin and our need for salvation by grace through faith in the Lord Jesus Christ. The Gospel does not only condemn sin but also self-righteousness which the Law does not save a man from sin but shows the need to be saved from sin. Romans 3:31 declares that the Law is not made void by faith but rather faith establishes the Law.