Peccability teaches that Jesus was able not to sin. Thus, it is implied that Jesus had the ability to sin or not to sin. The argument for peccability is made on the idea that the temptation to sin was only genuine if it were possible for Jesus to sin. Those who hold this view claim that if Jesus could not sin, the temptation was unreal, and therefore, Jesus cannot sympathize with His people.
Impeccability teaches that Jesus was not able to sin. Thus, Jesus could not sin. The capability for sin has nothing to do with the genuineness of a temptation. In the case of Jesus, the purpose of the various temptations was to demonstrate that Jesus was sinless and that He was the Son of God. As well, one must consider that it was not Satan who initiated the temptation, but the Holy Spirit.
- Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil. - Matthew 4:1
If Jesus were able to sin, then the Holy Spirit would be guilty of inviting Him to sin, which is something that God cannot do.
- Let no one say when he is tempted, I am being tempted by God; for God cannot be tempted by evil, and He Himself does not tempt anyone. - James 1:13