Why did Jesus fulfill the demands of the Law on the cross?
Christ fulfilled the Law's demands on the cross because the cross was an act of divine love. God's love for mankind nailed Him to the cross, and that love epitomized the Law's intent, so He fulfilled its demands. Thus love, not legalism, accomplished what the Law required.
Les teaches from Romans 13 that love is the fulfillment of the Law: “he that loveth another hath already fulfilled the law.” He explains that the work of the Cross was love—love epitomized. It was God’s love for mankind that nailed Him to the Cross, and as a result He fulfilled the demands of the Law. The commandments against adultery, killing, stealing, false witness, and coveting, and any other commandment, are briefly comprehended in “thou shalt love thy neighbor as thyself.” This is not a legalistic, pressurized system, but believers have been set free; that freedom is not licensed. Under the Law of Love, we no longer want to break these commandments, and the indwelling Holy Spirit directs our thinking and actions, though we are not sinless or perfect.