For there is one God and one mediator between God and men, the man Christ Jesus (1 Timothy 2:5).
Christ’s mediation consists of three anointed offices:
(1) Prophet (2) Priest (3) King
These three offices are clearly seen in Isaiah 61:1, which Jesus pronounced now fulfilled (Luke 4:21).
The Spirit of the Lord God is upon me; because the Lord hath anointed me to preach good tidings unto the meek [as Prophet]; he hath sent me to bind up the brokenhearted [as Priest], to proclaim liberty to the captives, and the opening of the prison to them that are bound [as King].
These three offices were absolutely necessary in order for Christ to successfully fulfill the mission given Him by the Father.
That mission consisted of saving His people from their sins:
And she shall bring forth a son, and thou shalt call his name Jesus: for he shall save his people from their sins (Matthew 1:21).
To do so would cost Christ His life:
Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many (Matthew 20:28).
It also consisted in the directive that He lose none given Him by the Father:
And this is the Father’s will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day (John 6:39).
Christ’s offices must complement each other as to design, intent and extent.
To do otherwise would be contradictory and illogical, introducing confusion into the perfection of God’s plan of salvation.
Christ’s offices must also perfectly fulfill the will of the Father, for anything outside the perfect revealed will of God is sin.
And Christ has never, will never, and can never sin (2 Cor. 5:21).
Christ always obeys the Father completely and absolutely (John 5:30).
I say these things to lay a foundation in answering the question raised in the this post.
Contrary to Scripture, there are innumerable serious, sober and sincere Christians who fervently believe and teach Christ died on behalf of all mankind.
They base their theology on the presumption that God loves all mankind equally.
For if God did not send His Son to be a propitiation for the sins of all mankind, it would be implausible to believe God loves those He intentionally denied the efficacious acquisition and application of Christ’s gracious atoning sacrifice.
And since ‘God is love,’ who ‘so loved the world,’ innumerable serious, sober and sincere Christians use these two verses as the ultimate proof texts by which they attempt to confound and refute those doctrines of grace which they so thoroughly abhor and detest, though they have been embraced by innumerable other serious, sober and sincere Christians throughout history.
As Mediator, Christ reconciles God and men.
For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life (Romans 5:10).
Reconciliation brings peace between parties at enmity with one other.
Christ brings peace between God offended and man offending.
Therefore being justified by faith, we have peace with God through our Lord Jesus Christ (Romans 5:1).
But there is no peace for the wicked:
There is no peace, says the LORD, for the wicked (Isaiah 48:22).
Neither Jew nor Gentile have, by natural means, known the way of peace (Romans 3:17).
Neither do they, by nature, seek the Lord, who is the way of peace (Romans 3:11).
It was revealed to the nation of Israel that salvation was of the Lord (Psalm 3:8; 27:1; Jonah 2:9).
With the exception of a minority of Elect Gentiles, the majority were not so graciously enlightened, and were instead intentionally left to die in their sins (1 Peter 3:20).
Even within the nation of Israel, only the Elect, the children of the promise, were given the saving revelation of the Messiah to come, the rest blinded that they might die in their sins (Romans 9:6-8; 11:7).
CONCLUSION: The essential purpose in Christ’s mission as Mediator was to reconcile enemies, bringing peace between God and men.
But not all men are reconciled to God.
Either it was never God’s intent to reconcile all men to Him, or it was God’s intent which He failed to accomplish.
But God never fails at achieving His purposes (Isaiah 46:10).
Either Christ failed in His mission of reconciliation or He was 100% successful.
If Christ failed by losing one person, He failed to do the will of His Father, who was adamant Christ lose none (John 6:39).
But Christ loses none (John 17:4, 12).
Therefore, it was never the Father’s intention to send Christ as Mediator to all mankind, but rather to those specific sinners elected by Him as the undeserving recipients of saving, reconciling grace.
And Christ’s mediatiation is 100% efficacious in achieving reconciliation with those whom God eternally willed peace.