In chapter 10 of his letter to the Romans, Paul refers to some people who have rejected the message of Jesus: “I can say that they are enthusiastic for God, but their understanding is not good. They have not submitted to God’s righteousness because they are ignorant of it and try to establish a righteousness of their own. Christ is the fulfilment of the law, making everyone who believes righteous.”
Unfortunately it is not just people who have consciously rejected the message of Jesus that “try to establish a righteousness of their own”. God’s idea of righteousness is not something that you can control, and so it is very tempting to try to create your own moral system. Jesus says, “Love your neighbour;” we say that means we have to be pleasant but we can otherwise feel free to ignore them. Jesus says, “You cannot serve God and money;” we say that means you can’t lust after money but you can be free to like it a lot.
The problem is that the little righteousness system that we create is more a reflection of us than it is of Jesus. You can’t get to heaven by following any human righteousness system. The only path to reconciliation with God is through Jesus, because Jesus, in his death on the cross to pay the price for our sins, has fulfilled all of the requirements of God’s righteousness system. There is nothing we can do to change that, and so our own righteousness systems are worthless.