The answer to this question revolves around the fact of the two natures of Christ. If he had been just a sinless man, then his destiny would have been that of Adam and all the rest of humanity, but due to the fact He was also God who cannot sin as absolute holiness and infinite righteousness, etc., the possibility is simply not there.
I have included below, a short overview of the doctrine of Christ’s impeccability. It really deals with the question of whether or not He was peccable (capable of sinning) or impeccable (incapable of sinning).
The Impeccability of Christ
The Fact of Christ’s Sinlessness
(1) Hebrews 4:15 reads, “For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin.”
(2) In addition Peter spoke of Him as a lamb unblemished and spotless (1 Pet. 1:19).
(3) Paul wrote in 2 Cor. 5:21 that “He became sin for us, He who knew no sin.”
(4) And in Hebrews 7:22-28 emphasis is made on the perfection of Christ’s ministry and sacrifice based on His eternal person and holy sacrifice as our sinless substitute. Here the statement is made: “For it was fitting that we should have such a high priest, holy, innocent, undefiled, separated from sinners and exalted above the heavens; who does not need daily, like those high priests, to offer up sacrifices, first for His own sins, and then for the sins of the people, because this He did once for all when He offered up Himself. For the Law appoints men as high priests who are weak, but the word of the oath, which came after the Law, appoints a Son, made perfect forever” (vss. 26-28)
Hebrews 2:10: perfect through suffering. It was not that Christ had been morally or spiritually imperfect, but his incarnation was completed (perfected) when he experienced human suffering. He identified with us on the deepest level of anguish, and so became qualified to pay the price for our sinful imperfection so that He could become a sympathetic High Priest. There is no thought of imperfection in the use of the word “perfect” in Hebrews in connection with the person and work of Christ. Rather, the point is through Christ’s person as the God-man Savior and through His temptations (which proved Him sinless), and through His sufferings and the offering of Himself as the perfect God-man Savior (true humanity and undiminished deity) He became the perfect solution and sacrifice for sin.
1 John 3:5 reads, “. . . and in Him there is no sin.”
The Question: Could Christ have sinned?
Christ was clearly sinless, was without a sinful nature, and was genuinely tempted, but the issue is could He have sinned? Some argue that if it was impossible for Christ to have sinned, then how could he have genuinely been tempted so that He could truly sympathize with our temptations?
Meaning of the Terms
Peccability: The view that Christ could have sinned is termed peccability from a Latin word, pecare, “to sin;” Peccability means, “able to sin.” The view that Christ could not have sinned is designated impeccability, “not able to sin.” Among evangelicals the issue is not whether or not Christ sinned; all evangelicals affirm His sinlessness. The question is, could Christ have sinned? Generally, most Calvinist’s believe that Christ could not have sinned, whereas Arminians generally believe that Christ could have sinned but did not.
Impeccability: Christ was genuinely tempted and in all points as we are (as in the temptation with Satan), but without any possibility of actually sinning (cf. Jam. 1:13). He was not able to sin, but this does not mean merely that Christ was able not to sin which implies that He might have been able to sin.
Those who hold to the peccability of Christ do so on the basis of Hebrews 4:15. As mentioned, they object claiming that if Christ was unable to sin, He could not have been tempted genuinely and therefore could not be a sympathetic High Priest (Heb. 4:15). The weakness of this view is that it does not sufficiently consider the total person of Christ as the God-Man Savior, true humanity and undiminished deity in one person.
Answer to this Objection
The reality of testing does not lie in the moral nature of the one tested, and the possibility of sympathizing does not depend on a one-to-one correspondence in the problems faced. Interestingly, the word temptation is used of both God the Father and the Holy Spirit (Acts 15:10; 1 Cor. 10:9; Heb. 3:9 and Acts 5:9), but no one would ever say the Father and Holy Spirit could have sinned.
As man, Christ was peccable; but as God, He was impeccable. Though Christ had two natures, he was one person and could not divorce Himself of His deity. Wherever He went and whatever He did, both natures were present. Therefore, since from the divine side Christ was immutable or unchangeable (Heb. 13:8), omnipotent (Matt. 28:18), and omniscient (John 2:25), it was impossible for Him to sin as God (Jam. 1:13) though He could be genuinely tempted as man.
(1) Testing demonstrated the sinlessness of Christ. The purpose of the temptation was not to see if Christ could sin, but to show that He could not and did not sin. His temptation showed what a unique Savior He was and that He was qualified to pay the penalty for all the world.
(2) Testing made Him sensitive to the pressure of testings or temptation and thus a sympathizing High Priest.
(3) Testing demonstrated that He is perfect example for us of victory over the most difficult kinds of tests.