5:19
So how does God reconcile the world to Himself? It is in Christ and it entails not counting our sins against us. The gospel is not just that “God loves us”. This is a far too wooly and unbiblical picture, and a rather meaningless one. The starting point of the gospel is that we have sinned against God, this goes right back to Genesis 3, and all of us have been living in rebellion ever since. Sometimes people object to the church saying that certain things are sinful, as though a certain group of people were being singled out. This is nonsense, for all have sinned (Rom 3:23). We are all sinners, all in need of forgiveness, and all can receive that forgiveness through faith in Christ. This is the message of reconciliation that has been committed to us. We should also note that since the root problem is the need for us to be reconciled to God, it is God who sets the terms of reconciliation, and we have no right to change those terms.
5:20
Being a “minister” of the gospel in any sense at all is not a matter of doing things our way, or representing our own ideas. We are “Christ’s ambassadors”. An ambassador represents the interests of the party he is representing, not his own interests. A good ambassador will use initiative and skill, but he or she uses it in the interests of the party they are representing. So we work as though God were making His appeal through us. So we “implore on Christ;s behalf: Be reconciled to God”. This is the message, the appeal. It means we have no authority to abandon the things that God has said that He cares about.
5:21
The gospel is all about dealing with the problem of human sinfulness. How did God do this? He made “him who had no sin to be sin for us”. Our sin was placed upon Christ and He took the judgement that should have been ours. That is the means, the goal is that we “become the righteousness of God”. What does it mean to say we are the “righteousness of God”? It can be looked at in a forensic sense and a transformative sense, and I think we need to take both. Man is always trying to prove himself “righteous” (though often he will not use that term), he tries to prove himself “good enough”. In common parlance, most people think they are “basically good”. But this will not impress God! It is Christ, His death and resurrection, alone that makes us righteous. So in a forensic sense we are declared righteous because of Christ. But we are also being transformed, and on the last day will be made perfect. Moreover, you cannot separate the two, and the Bible does not separate the two (though at times it may focus more on one than the other).