The righteousness of God

"When we display our righteous deeds, they are nothing but filthy rags."
Isaiah 64:6

“God made him who had no sin to be sin for us, so that in him we might become the righteousness of God.”- 2 Corinthians 5:21

See, the key difference is this: OUR righteousness and HIS righteousness.

Our righteousness, every good thing we do in and of ourselves, is nothing but filth, because it is apart from Christ. But "in him," in Christ Jesus, when we abide in him, not only do we possess HIS righteousness, we BECOME the righteousness of God. So, I think Jesus's death and resurrection, the forgiveness of sins and justification, goes maybe a step further. So that "we might become the righteousness of God."

just another way that we are to become like God, conformed to not only His will, but His image, His heart.