At the core of the Christian Gospel, it has been revealed to mankind that the one true God of the universe is perfectly righteous in every respect, in all that He does, and that humans are innately unrighteous. Because of the fall of mankind in the Garden of Eden, we no longer have an intact relationship with God by default of being one of his created humans; He and His ways are flawless perfection, and therefore, His standards of relationship require the same, which humans fall terribly short of.
The first definition that Webster's Dictionary gives to define righteousness is: "to act in accord with divine or moral law: free from guilt or sin." To seek to be righteous is to attempt to conduct all of one's thoughts and actions so that no fault can be found inside, or outside, the person. From strictly a human viewpoint, it is possible for us to do good deeds apart from God that have no obvious or visible blemishes of sin or evil. However, it is not possible for us to do good deeds with irreproachable motives, nor is it possible to do only good deeds, and do them continuously, without eventually doing wrong. In addition to this, it is also true that before the intent to even start doing good is begun, all humans have a grimy, mistake-ridden past that we would rather not acknowledge, even to ourselves, which causes the entire endeavor of pursuing righteousness to be fatally flawed before it's begun.
Most of mankind in our age assents to the following philosophy: a good deed can be entirely good, and therefore, while we may not be perfect, we certainly are not all that bad, or not as bad as some people, and sometimes we are good, and so perhaps even "righteous." It's at least a consistent hypothesis, except that it only compares bad people to bad people — there is no sample group of good people. This paradigm of right and wrong takes no account of how fallen we are on the inside; that if we should seek to do good deeds, we are still operating from a disposition of pride, selfishness or another similar human attitude or frame of mind and heart. We can't do it. Jesus revealed this to mankind with some examples that magnify the concept of our depravity, and drug it tumultuously struggling, into plain sight and to our attention. In one such example, the story of the rich young ruler, the wealthy young man's thoughts were on what he could accomplish to gain God's approval. The rich young ruler asked, "...Teacher, what good thing shall I do that I may obtain eternal life?" (see: Matthew 19:16-26). This man's focus was on what he could do in the power of his own sinful nature, a nature of which God tells us is only capable of evil: "...and that every intent of the thoughts of his heart were only evil, continually" (Genesis 6:6). Jesus spoke towards a correction of thought, illustrating that no increased level of "performance" or "good work" can have a high-enough appraisal of value with regards to earning God's approval. Being divine, Jesus saw this man's inward desires and thoughts, and made a request of the rich young ruler, tailored to confront the most precious object of his heart — his wealth — and then directed the logical momentum of the conversation towards the only potential alternative, an alien righteousness, viz. himself, the Christ. "'...All these things I have kept; what am I still lacking?' Jesus said to him, 'If you wish to be complete, go and sell your possessions and give to the poor, and you will have treasure in heaven; and come, follow Me.'" (Matthew 19:20-21). Christ's most dedicated followers even abandoned Him when He was arrested and prosecuted. We can't do it. We need an alien righteousness; we need a righteousness outside of ourselves.