God's righteousness is an integral part of His character, and He can never do anything unrighteous. He cannot be partial or show favouritism towards someone because that would be unrighteous. In all He does, He has to be righteous. Sometimes we people do not think of God like this, because people usually imagine that if we love someone, we can be justified if we bend the rules, such as telling a lie, in order to show 'love'.
Just look at one example of how this works out for God. Without any exception, all human beings have sinned, and we all fall short of His standards so that God cannot accept any of us and be still righteous about it. If He just decided to forgive us, it would be unrighteous and unjust because we ought to be punished. We know the way He worked this out. He saw to it that our sins were punished, by placing them on Jesus and getting Him crucified. We can go to God on those terms, by accepting the fact that we deserve punishment for our sins and receiving forgiveness freely through the death of Jesus in our place. If God just forgave everyone because He loves them, as some think, but they would not go through Jesus for salvation, it would be unrighteous.
Now think of another way in which the righteousness of God is manifested in our salvation. Here we were lost in sin, with no way to work our way back to Him through pilgrimage, penance, sacrifices, rituals, or anything else we could do. It would have been unrighteous of God if He gave us the Law and expected us to keep it and find our acceptance with Him, because we could not. So, while we see that it was God's undeserving love towards us that made the way of salvation through Jesus, we can also see that He was manifesting His righteousness also through it! "But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets, even the righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction; for all have sinned and fall short of the glory of God, being justified as a gift by His grace through the redemption which is in Christ Jesus" (Rom.3:21-24).
After receiving this salvation freely as a gift from God, if we went about sinning as usual, or living for ourselves or to enjoy our life on earth, will that be righteous from our part? There is a huge difference between someone trying not to sin in any way and still falling here or there because of ignorance or weakness, and another man thinking that God's grace will cover for him and living an unconverted or compromising life. The second man is trying to take advantage of God's grace, and that is to be quite unrighteous!
"Lovingkindness and truth have met together; Righteousness and peace have kissed each other" (Ps.85:10). God makes this happen through the way of salvation He offers through Jesus. Let's not forget it's not lovingkindness alone that is at work, but also truth and righteousness.
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