How do we know Christ's righteousness is necessary?

The necessity of Christ's righteousness stems from the nature of God's law and the condition of humanity post-fall. In the Old Testament, priests could not wear wool because it symbolized sweat, which is associated with man's sinfulness and rebellion against God. Only linen garments were permitted, which signify purity. Christ, however, bore our guilt and provided righteousness by fulfilling the law perfectly on our behalf, exemplified in His obedience leading up to the Cross. His righteous acts cover believers, effectively allowing them to stand justified before God.