Paul is simply personifying sin in referencing the sin offering of Jesus.
2Co 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
A parallel verse to that is this...
Rom 8:3 For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
Sin is a moral issue as opposed to something physically tangible. One cannot be "made sin" in a literal sense, nor can "flesh" be described as "sinful." Paul is given emphasis with his use of language. Jesus would do the same thing and a good example was when Jesus told people that they had to eat his flesh and drink his blood.
Take a look at 2Cor 5:21 carefully, especially in the context of the surrounding verses.
2Co 5:13 For whether we be beside ourselves, it is to God: or whether we be sober, it is for your cause.
2Co 5:14 For the love of Christ constraineth us; because we thus judge, that if one died for all, then were all dead:
2Co 5:15 And that he died for all, that they which live should not henceforth live unto themselves, but unto him which died for them, and rose again.
2Co 5:16 Wherefore henceforth know we no man after the flesh: yea, though we have known Christ after the flesh, yet now henceforth know we him no more.
2Co 5:17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
2Co 5:18 And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
2Co 5:19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
2Co 5:20 Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God.
2Co 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
2Co 6:1 We then, as workers together with him, beseech you also that ye receive not the grace of God in vain.
2Co 6:2 (For he saith, I have heard thee in a time accepted, and in the day of salvation have I succoured thee: behold, now is the accepted time; behold, now is the day of salvation.)
2Co 6:3 Giving no offence in any thing, that the ministry be not blamed:
2Co 6:4 But in all things approving ourselves as the ministers of God, in much patience, in afflictions, in necessities, in distresses,
2Co 6:5 In stripes, in imprisonments, in tumults, in labours, in watchings, in fastings;
2Co 6:6 By pureness, by knowledge, by longsuffering, by kindness, by the Holy Ghost, by love unfeigned,
2Co 6:7 By the word of truth, by the power of God, by the armour of righteousness on the right hand and on the left,
2Co 6:8 By honour and dishonour, by evil report and good report: as deceivers, and yet true;
2Co 6:9 As unknown, and yet well known; as dying, and, behold, we live; as chastened, and not killed;
2Co 6:10 As sorrowful, yet alway rejoicing; as poor, yet making many rich; as having nothing, and yet possessing all things.
2Co 6:11 O ye Corinthians, our mouth is open unto you, our heart is enlarged.
In the above passage Paul is presenting the "Ministry of Reconciliation" and one of the key verses is...
2Co 5:15 And that he died for all, that they which live should not henceforth live unto themselves, but unto him which died for them, and rose again.
...which is a parallel too..
Rom 8:3 For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
Rom 8:4 That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
...which is a parallel too...
1Pe 2:24 Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed.
...which is a parallel too...
Rom 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Rom 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Rom 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
Rom 6:7 For he that is dead is freed from sin.
"Jesus being made sin for us" is simply Paul expressing that Jesus offered himself on our behalf for the express purpose that "we be made the righteousness of God in Him" and this occurs via...
2Co 6:1 We then, as workers together with him, beseech you also that ye receive not the grace of God in vain.
When any individual truly repents (dies to sin in tbe baptism of repentance) and is raised up to new life in order to walk in the Spirit of life in Jesus Christ, that individual is made the righteousness of God in Christ. The righteousness of the law is fullfilled in us through the dynamic of grace through faith (ie. abiding/walking/existing in accordance with the divine influence of God upon our hearts.
The law was merely a shadow of love and the focus of the New Testament is exclusively on the SOURCE not the shadow, hence those whom walk after the Spirit are not under the law.
Many false teachers today pervert 2Cor 5:21 by isolating it from its context (especially via hiding 2Cor 6:1) and present it as a statement representing a POSITIONAL LEGAL TRANSACTION which has NOTHING TO DO WITH A LITERAL INNER TRANSFORMATION.
Thus a perverted gospel message of mere "trust in a provision" is promoted which is completely absent of the actual WORKING DYNAMIC which brings an authentic regeneration to the Christian. Thus an unregenerate individual is able to claim that they are "made the righteousness of God in Him" whilst they are still in the service of sin (still in rebellion to God/still engaging in known evil).
