Galatians 3:13 was written in reference to Deuteronomy 21:23: "His body shall not remain all night upon the tree, but thou shalt in any wise bury him that day; (for he that is hanged is accursed of God
that thy land be not defiled, which the LORD thy God giveth thee for an inheritance." (KJV)
That Jesus was called sinless is recorded in the New Testament. Hebrews 4:14-15; 7:26; 1 Peter 1:19; 2:21-24; read Isaiah 53:1-12 for an explanation of a man to come. As Jesus was called sinless, this places him in a special category. Paul states that we "all have sinned, and come short of the glory of God." (Romans 3:23). No matter where we are, in geographical terms or time (place of existence' e.g., century), we have sinned or have broken some divine law (see 1 John 3:4).
Therefore, having broken a divine law, justice demands payment or restitution from the offender. Today, whenever someone breaks our criminal laws, the offender is tried, sentenced and remanded to jail or prison, where the offender will remain until the law is satisfied. Likewise, divine law demands that someone pay the debt. Unless we are willing to pay that penalty ourselves, we would surely desire a savior or someone else to pay that godly debt. Hence, Jesus is called a Savior for that reason: He will save us from our sins.
Jesus was called to be the person upon whom the LAW could be exacted. How painful is God's punishment? We may not wish to find out. Therefore, Jesus became the lightning rod for the sins of those who believe on Him. "He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God." (John 3:18). He or she that does not believe it appears will pay for their own sins. For all those who believe in the Son of God will receive protection from the wrath of the LAW, so He became a "curse"
Sin is no curse, death is no curse, the law became a curse for us because we could not keep it. so in what sense he became a "curse"
for us so He could pay the penalty. And since the LAW could have no hold upon Him because He broke no law, He could pay the penalty willingly. "Therefore doth my Father love me, because I lay down my life, that I might take it again." (John 10:17). Any person who has broken the law (whether ours or God's) cannot get out of prison until the sentence is finished. So we cannot help anyone else because we are all in the same predicament. Jesus therefore being a free Being can come into our prisons and free us if we are willing to believe and do as He asks. It is not enough to be set free, we must do as Jesus bids. "If any man serve me, let him follow me." (John 12:26).
It takes time and study to fathom the meaning of the words found in scripture, since they speak of things beyond our ordinary experiences. If you are one of the fortunate few to have been favored of God and received divine inspiration or the ability to comprehend the deep import of these words, then you are fortunate indeed for the rest of humanity relies upon ordinary scholarship for its understanding.