Let me offer another perspective…
Had Christ given into the temptation of the Devil, and had He done what the Devil asked of Him, He would be giving undeniable proof of His divinity. However, as St. Chrysostom writes:
“How does [the Devil] expect to discover by this proposition whether He be the Son of God or not? For to fly through the air is not proper to the Divine nature, for it is not useful to any. If then any were to attempt to fly when challenged to it, he would be acting from ostentation, and would belong rather to the Devil than to God. If it is enough to a wise man to be what he is, and he has no wish to seem what he is not, how much more should the Son of God hold it not necessary to shew what He is; He of whom none can know so much as He is in Himself?”
Because it is not proper to the divine nature for Christ to boldly proclaim His divinity in the ways suggested by the Devil, He was incapable of doing this. Thus, it was not possible for Him to give into the Devil’s temptation, because it would contradict the divine nature. And likewise, being a perfect Man as well, His human will must be fully in accordance with the divine will (as it is with all those in heaven), and as such, He could not sin.
I need to think about this more; I’m open to correction, especially from a priest.