Christ’s atoning death is clearly connected with His advocacy before the Father. Therefore, we can see the following truths:
1) It is impossible that the Son would not intercede for everyone for whom He died. If Christ dies as their Substitute, how could He not present His sacrifice in their stead before the Father? Can we really believe that Christ would die for someone that He did not intend to save?
2) It is impossible that anyone for whom the Son did not die could receive Christ’s intercession. If Christ did not die in behalf of a certain individual, how could Christ intercede for that individual, since He would have no grounds upon which to seek the Father’s mercy?
3) It is impossible that anyone for whom the Son intercedes could be lost. Can we imagine the Son pleading before the Father, presenting His perfect atonement in behalf of an individual that He wishes to save, and the Father rejecting the Son’s intercession? The Father always hears the Son (John 11:42). Would He not hear the Son’s pleas in behalf of all that the Son desires to save? Furthermore, if we believe that Christ can intercede for someone that the Father will not save, then we must believe either 1) that there is dissension in the Godhead, the Father desiring one thing, the Son another, or 2) that the Father is incapable of doing what the Son desires Him to do. Both positions are utterly impossible.
That Christ does not act as High Priest for all men is clearly seen in His “High Priestly Prayer” in John 17. The Lord clearly distinguishes between the “world” and those who are His throughout the prayer, and verse 9 makes our point very strongly:
I pray for them. I am not praying for the world, but for those you have given me, for they are yours.
When Christ prays to the Father, He does not pray for the “world” but for those that have been given to Him by the Father (John 6:37).
The entire article deserves a read and is a great supplement to this series on Hebrews.