Why was it necessary for Christ to humble himself even "unto death"?

Because with respect to the justice and truth of God, (a) satisfaction for our sins could be made no otherwise, than by the death of the Son of God. (b)

(a) Gen.2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die. (b) Rom.8:3 For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh: Rom.8:4 That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit. Heb.2:9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man. Heb.2:14 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil; Heb.2:15 And deliver them who through fear of death were all their lifetime subject to bondage.