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I would say that the explanation for the servant's suffering is contained in the verse cited in the question (Isaiah 53:10), which indicates that it was meant by God to make a sufficient atonement (that is, to pay the full penalty) for the sins of all humanity from eternity past to eternity future. The willing endurance of this undeserved suffering by the servant (that is, Christ), in turn (and as also described in the same verse) caused God to take pleasure in Him and to prolong His days (through His resurrection), as well as enabling Christ Himself to see the multitudes who would subsequently be saved through faith in Him.. The author of Hebrews later spoke of the same willing endurance (as well as the motive for it) in Hebrews 12:2.
This is what John Phillips calls "the unfathomable mystery of Calvary"--"it pleased the LORD to bruise him" (under his heading, THE TRAGEDY OF THE CROSS REVIEWED). His death was determined beforehand by God (Acts 2:22–23). Compare what Dr. Luke says in Acts 4:27 “For indeed both Herod and Pontius Pilate, with the Gentiles and the people of Israel, assembled together in this city against your holy servant Jesus, whom you anointed, 4:28 to do as much as your power and your plan had decided beforehand would happen. [NET] It means that Jesus took the sins that, still today, twist your guts in a painful knot. He did this after they twisted a crown of thorns for the sacred head now wounded for our transgressions and bruised for our iniquities. This was the Father's will, it pleased the Lord [God the Father] to bruise him (His Son). There you have it, my friends. God caused His servant to suffer so because He decided it would be best. The Father knows best! It was THE ONLY WAY to bring about our redemption.
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