Webster's parses the word 'impeccable' into two parts; 'not' and 'to sin'. While most who profess Christ as their Savior will readily state that Jesus Christ did not sin, it seems a small and growing number claim that it was possible for Him to have sinned while on earth. They conjure up any number of reasons for this but the root of all their words is an ignorance of the Character of Christ (both human and Divine) and a willingness to find fault rather than an occasion for praise to the One they claim to love and serve. Such a suggestion that Christ "could" have sinned originates from the same spirit who said: "Yea, hath God said" Gen. 3:1.
A year or so after the Lord saved me I was in a "Precept" class studying Romans. The teacher began one class with his 'off topic' statement (not found in the study guide) that it was possible for Jesus Christ to have committed sin while on earth. It felt like my heart was going to come up through my throat as I heard him speak. One of the first words out of my mouth was 'heresy' as I could not stand to hear his nonsense anymore. At the time I did not know the Scriptures that would totally dismantle this heretical doctrine so I asked the pastor whose only answer was John 10:30, "I and My Father are one." A good place to start, but hardly the only verse that addresses this lie. The Lord began to show me other verses over the months and years after this as to prepare me to be able to give at least an adequate answer should it ever come up again. It did. This same man, now chairman of the deacons of this SBC "church", was going to teach a class that I attended so I asked him if he still believed and taught that 'it was possible for Jesus to have sinned while on earth.' His response: "I NEVER taught that", which was a bald-faced lie. What ensued after this lead to my departure from that "church" on less than amicable terms (I was told to either "shut up", "leave", "or be forcibly removed" by a group of six 'leaders' of this 'church' as they were shy their "senior pastor" who had left under not so good circumstances forced on him by the 'old guard' of that 'church.' [As for the "Precept" courses and their author, Kay Arthur, stay as far away from all of that as you can. The courses are shallow at the very best, rife with false doctrine that stems from the 'free will' heresy, and caters to the flesh offering only cursory, fake, 'praise' to the Lord Jesus. KA is highly ecumenical.]
The following verses are far from an exhaustive treatise of this matter but are offered as a starting point with the encouragement to further study. As stated previously, to say that Jesus Christ did not sin is no doubt true, but leaving the door open for the "possibility" that He "could have sinned" is a class of heresy all to itself. It has taken root in too many places and is one of those 'stealth' false doctrines that gets limited, if any, 'air time' having become one of the unwritten and unspoken tenets of evil men. But some are bold in their assertion that Jesus could have sinned and have acquired a large following. Don't be afraid to ask your pastor or favorite teacher what their stance is on this matter.
Beginning in James 1:13-16: "Let no one say when he is tempted, 'I am tempted by God'; for God cannot be tempted by evil, nor does He Himself tempt anyone." The last phrase 'nor does He Himself tempt anyone' implies "with sin, or evil." Jesus Christ, the Son of God, the Son of Man, both 'personalities' living in the same physical body, at the same time, collectively and individually impervious to sin. Some may object and ask "what about the 'man' side of Jesus?" Fair question. Luke 1:26-35 tells of the birth of Christ was without a human father, via the Virgin Mary. With no human father, the sin of Adam was not, could not, have been imputed to Christ as it is with every other man, Rom. 5:14-21. There was no human sin nature in the Man Christ Jesus. Pure human, pure God, no sin nature, and therefore impossible for Him to be "tempted" or drawn to sin with the intent or end result to commit any sin. John 14:30 weighs in with this: "...for the prince of this world is coming and has nothing in Me." There was nothing in the Lord Jesus to give even a 'foothold' to the wicked one to make Him sin. "Ah, but Heb. 4:15 says that Jesus was tempted in all points as we are, what about that?" He no doubt was, and just as surely more so than we as seen in Matt. 4:1-11 and "yet without sin." Note His answers were always direct quotes from the Word of God. The 'testing' of the Lord Jesus resulted in two things: proof that He did not sin, no matter what was placed in front of Him, and proof that there was nothing in Him that would draw Him to disobey His Father, there was no sin nature to overcome and therefore no propensity for sin. James 1:14 shows the cause of human sin "...each one is drawn away by his own lust, and enticed." Since there is no such "lust" in Christ Jesus, there is nothing by which to 'entice' Him into sin---no sin nature. The key here is to understand and know that the Lord Jesus had no sin nature as is common to men, but a human nature not plagued with sin, or lust, or anything other than a heart set on doing the will of His Father.
This is a dangerous game of "what if" that some men play, not considering the outcome of any supposed "sin" that "may" have had the "possibility" of being committed by the Lord Jesus. Consider John 8:28 & 29. "...I do nothing of Myself..." So by whom does the Lord Jesus act? The Father? The Holy Spirit? Both. Continuing in John 8; "...but as My Father taught Me, I speak these things. And He who sent Me is with Me. The Father has not left Me alone, for I always do those things that please Him." In order to say that it was "possible" for the Lord Jesus to sin, that statement must include as complicit partners the Father and the Holy Spirit. If Jesus and His Father are one (John10:30), then it follows that if Jesus "could have sinned" this must include the Father as well. As I said, a dangerous game. Would the Holy Spirit be excluded from this never ending web of deceit? Hardly, hence the danger grows to include blaspheme against the Holy Spirit---the only unpardonable sin. IF there were sin it would be multiplied by the fact that John 8: 28 & 29 now turn into a lie---another sin, and the dominoes just keep crashing down. Unrighteousness would be found in the Trinity, negating John 7:18. It becomes a never ending ploy to cast doubt in the mind of anyone who seeks the truth---one of the most used tools of the wicked one. Further, Heb. 1:3 says that Christ "is the express image of His [the Father's] person." Would these purveyors of deceit further claim that it would be possible for the Father to sin? That is exactly what they are saying, even if they do not realize it. Heb. 13:8 says: "Jesus Christ, the same yesterday, today, forever." If it be true that He 'could have sinned' while on earth why not for all eternity? He never changes---except in the evil imaginations of wicked men. How could He offer Himself as the Spotless Lamb if a possibility of sin lingers at the door? He would no longer be spotless, but covered in question marks. It could not be said of Him, or His Father, or the Holy Spirit that they are incorruptible (Rom.1:23) if sin were even a possibility. No longer could we say "Far be it from God to do wickedness" Job 34:10. We could no longer shout with the Psalmist "To declare that the Lord is upright; He is my rock, and there is no unrighteousness in Him." Psa. 92;15
In order for anyone to sin there must be something within his character that makes it possible. Humans are locked in to sin, even their "free will" cannot extract them from the ravages of the sequence of sin: "But each one is tempted when he is drawn away by his own lust and enticed. Then when desire has conceived, it gives birth to sin; and sin, when it is full grown, brings forth death. Do not be deceived, my beloved brethren." According to these words sin MUST have a place of conception, a willingness to do evil. Somehow, they perceive that such was the case with the Lord Jesus Christ. They have concluded that He is just like they are in regard to sin, an easy mark. They have no clue as to the Character of the Lord Jesus, human or Divine. The 'possibility' of Christ sinning serves no purpose other than that of His enemy, the devil, using this lie to cast doubt in the minds of many thereby stunting their growth in Christ until the lie is exposed to them.
Luke 24: 32 & 45
"Afresh, precious, precious Jesus, I resign this body to You, for doing or suffering, for living or dying. Will You accept it? Will You use me for Your glory more than heretofore, that You may have some little return for all the benefits You have done to me? Oh, do grant this request; my heart longs for it, my spirit pleads for it; and "if You will, You can." You know the hot temptation of which I am the subject. Bring Your glory out of it, and keep me from the evil, and it shall be well." - Ruth Bryan