The best theologians, past and present, have been divided on the question of whether Jesus could have sinned. I believe that since Jesus was fully human, it was possible for him to sin. Obviously, the divine nature cannot sin. But if Christ’s divine nature prevented him from sinning, in what sense did he obey the law of God as the second Adam? At his birth, Jesus’ human nature was exactly the same as Adam’s before the fall, with respect to his moral capabilities. Jesus had what Augustine called the posse peccare and the posse non peccare, that is, the ability to sin and the ability not to sin. Adam sinned; Jesus did not. Satan did everything in his power to corrupt Jesus and tempt him to sin. That would have been an exercise in futility had he been trying to tempt a divine person to sin. Satan was not trying to get God to sin. He was trying to get the human nature of Christ to sin, so that he would not be qualified to be the Savior.

At the same time, Christ was uniquely sanctified and ministered to by the Holy Spirit. In order to sin, a person must have a desire for sin. But Jesus’ human nature throughout his life was marked by a zeal for righteousness. “My food is to do the will of Him who sent Me” (John 4:34), he said. As long as Jesus had no desire to sin, he would not sin. I may be wrong, but I think it is wrong to believe that Christ’s divine nature made it impossible for his human nature to sin. If that were the case, the temptation, the tests, and his assuming of the responsibility of the first Adam would have all been charades. This position protects the integrity of the authenticity of the human nature because it was the human nature that carried out the mission of the second Adam on our behalf. It was the human nature uniquely anointed beyond measure by the Holy Spirit.

https://www.ligonier.org/blog/could-jesus-have-sinned/

I was asked to comment on the impeccability of Christ. Sproul maintained that Christ could sin because if he can’t possibly sin, then he isn’t human. So, Sproul trying to maintain the Humanity of Christ argued for the peccability of Christ. That also assumes that a precondition for being human is the possibility of sin. Sproul hardly argues or shows that that is the case. Others point out that saints in heaven can no longer sin but remain human:

Unless one believes that the saints in heaven can still commit apostasy, a capacity to sin is not intrinsic to human nature.

http://triablogue.blogspot.com/2017/11/was-jesus-impeccable.html

Sproul appeals to Christ being the second Adam as a reason for why it is possible for Christ to fail while being under the Law. Why think the idea of Christ being the second Adam is about Christ succeeding where the first had failed? That the Second undoes the curse of the first? The second Adam doctrine shows the inferiority of Adam. Christ does what no mere man could do because he was never merely a man.

Satan tempting Jesus in the wilderness is his last piece of evidence to show that this view is Biblical. The problem is that Satan tried to tempt someone that couldn’t succumb to temptation. Even if that is Satan’s motivation, that doesn’t imply it is actually possible. Satan wishes to overthrow God and make himself God. Is that possible now?  Satan could also be tempting to see if this is the one prophesized through the OT. Christ merely was desiring things that are good(food, water, etc) but through sinful means as David Gadbois has stated:

It seems to me that it is often the case that we can feel the allure of sin because we are attracted to the good thing wrapped inside the sinful temptation. Satan offered Jesus food. The food is, itself, a good thing, but was wrapped in the temptation to acquire it through illegitimate means.

http://triablogue.blogspot.com/2017/11/was-jesus-impeccable.html

The Christology should recognize that while Christ’s human will/nature is not mixed and is distinct from his divine will/nature. That doesn’t mean the human side acts independently of the divine side.

Another issue is what does it mean that Jesus “could” sin? Sproul doesn’t quite unpack what he is actually stating. “Could”, “can”, and “ability” are a very ambiguous word in these regards. Philosophers have discussed this in other mediums:

And now, let PAP If instead be the principle that “a person is morally responsible for what he has done only if he could have done otherwise, had his inner desires inclined him to do so at the moment of choice.” This modified criterion no longer requires a categorical ability to do otherwise while holding all other things in place; rather, it is a conditional ability that is in view:133 if the person had wanted to, that is, if—contrary to fact—his heart and mind had inclined him to do so, could the person have followed up on these alternate desires and acted otherwise than he in fact did? If not, this newly introduced PAPIf would declare on that condition that he is not morally responsible. Note that this is not an attempt to define the words “can” or “ability,” so it should not be worrisome that the word “could” found its way again into my explanation. It is not a circular definition of the word, it is merely an attempt to capture one particular sense of ability—the conditional ability—that one can be said to have, if, assuming his desires were different, he could have acted on those desires and done otherwise. If, contrary to fact, the person had wanted to, would there have been something else besides his desires preventing him from executing the alternative course of action? If yes, the PAPIf declares that he is not morally responsible for his failure to do otherwise. In other words, PAPAll says that a categorical ability to do otherwise is necessary for moral responsibility, while PAPIf says that a conditional ability to do otherwise is necessary for moral responsibility.134 Once the ability is disambiguated as above, it becomes clear that of the two principles, only PAPAll is incompatible with determinism. If the alternate possibility must be accessible by the agent’s will all things being categorically just as they are, then it calls for indeterminism indeed. PAPIf on the other hand, is quite compatible with determinism, because its built-in condition “had his inner desires inclined him to do so” permits a hypothetical, counterfactual modification of the antecedents (namely, the state of heart and mind of the agent prior to the choice), and thus opens the door to an alternate possibility (an alternate choice) without necessitating indeterminism.

Bignon, Guillaume. Excusing Sinners and Blaming God: A Calvinist Assessment of Determinism, Moral Responsibility, and Divine Involvement in Evil (Princeton Theological Monograph Series Book 0) . Pickwick Publications, an Imprint of Wipf and Stock Publishers. Kindle Edition.

Let’s discuss the ways Christ could and couldn’t sin:

Physical and Psychological ability:

Christ could have sinned in this regard because he merely had all the physical capabilities to do so. He had arms, legs, and a fully functional mind. The only way to state Christ wasn’t physically able is to say that Christ had some kind of disability, sickness, or injury. I suppose these aren’t popular options.

Moral Ability:

Christ couldn’t have sinned because it isn’t in Christ’s moral disposition to sin.  He has a perfect character that doesn’t allow him to produce evil inclinations and sinful deeds.

Hypothetical Ability:

This is about whether there is some state of affairs in which Christ could sin. Can Christ sin in some possible world? I would state that this is impossible because of the hypostatic union.

Grant me the intuition that a maximally great person cannot possibly sin because they are morally perfect. Christ is a maximally great person. Therefore, Christ couldn’t possibly sin. If Christ is possibly sinful, then in some possible worlds Christ isn’t morally perfect. I am not sure if we could escape from radical skepticism at that point because Christ could simply deceive all mankind into thinking he is a savior. What are the Trinitarian implications? Is there some possible world where the Son is in rebellion to the Father qua his humanity? 

Further Suggestions:

Could Jesus sin?

Was Jesus impeccable?