John Chrysostom

In reality, the people were subject to another curse, which says, "Cursed is everyone who does not continue in all that is written in the book of the law." To this curse, I say, people were subject, for no person had continued in or was a keeper of the whole law. But Christ exchanged this curse for the other, "Cursed is every one that hangs on a tree." … It was necessary for him who is about to relieve us from a curse to be himself free of it. But he received another instead of ours. Therefore Christ took on himself just such curse and thereby relieved us from the curse. It was like an innocent person deciding to die for another sentenced to death, and so rescuing him from punishment. For Christ took on him not the curse of transgression but the other curse, in order to remove that of others. For "he had done no violence, neither was any deceit in his mouth."