"and be found in Him, not having my own righteousness from the law, but that which is through faith in Christ, the righteousness from God that depends on faith," -Philippians 3:9.
The Apostle Paul having been saved by faith in Jesus, understood the difference and the purpose for which God introduced the Law; that is, the Law of Moses. The Law was good, just and holy because it came from God.
The Law served several purposes, to stop the increase and practice of sin, to establish righteousness among men, and to lead men to God. The Law though good lacked in helping man to live perfectly as God pleases. The Law can only point out evil, it does not help you to do good.
Hence, God by sending Christ can do what we cannot do. That is, to live perfectly according to the Law. Paul says that the righteousness he possessed was that which was derived from the Law; in other words, that which he imitated from the Law, but not perfectly. In other words, his righteousness was not perfect.
Now, the righteousness that is received by faith is that which is not ours, but Christ's. Christ lives perfectly before God and lived perfectly in our place. Christ lives perfectly before God and lived perfectly in our place. Because of this, God gives the righteousness of Christ to all those who come to God by faith in Jesus.
When the Bible speaks of righteous people, it refers to actions that are in accordance with God's will. That which is good. But those people themselves are not righteous because they are born in sin. Only Christ is sinless and therefore righteous in Himself. God through faith gives us the righteousness of Christ and for eternity sees us in union with Christ. By Him we are justified from all our sins, and He sees us in Christ as if we had never sinned.
The reason is, God sees us through Christ, the One who never sinned, the Righteous, Holy, Perfect One. That is why we worship God and praise Him for His Grace and Mercy!