Answer:
I think it’s probable that he could (IE was capable of) sin. You clearly believe correctly that Jesus was fully God and fully man. But we tend to think of him as MORE God than man which is why your intellect is saying he could not sin. Now it’s true, he would not sin, but that doesn’t mean he could not. So our questions are, A) do we really believe Jesus was sinless and B) does this sinlessness mean he COULDN’T sin and C) how does knowing whether he could or couldn’t help us? Let’s answer these in order:
A) we have to decide if we believe the declarations in the Bible about Jesus. He himself made the bold statement that he was without sin. He challenged people to find him guilty of one in John 8:46. The only sin they could finally pin on him was blasphemy, because he made himself equal with God by calling himself God’s Son (10:33). Of course, that’s only a sin if it isn’t true! Also, people who lived with him for 3 years, who would have known him better than anyone, also confirmed his sinlessness (1 Peter 1:19; 1 John 2:1). So if we accept this record, then on to your main question:
B) Could Jesus sin? IE, was he capable of sin? We must assume by the fact that he was human that he COULD. Now, the Old Testament says several times, “God is not a man , that he should lie.” (Num 23:19) Meaning, God is not subject to human weakness and so we should always expect him to act according to his perfect, good, moral character – he cannot do otherwise. But of course, there came a moment, in the fullness of time, when the Father sent the Son, that God DID become subject to human weakness! Jesus was like us in every respect, the bible says, which must mean he had free will like us. But he did not abuse it like us. Heb 4:15 “This High Priest of ours understands our weaknesses, for he faced all of the same temptations we do, yet he did not sin.” NLT If Jesus understands our weakness, temptation could have worked. Was Satan merely playing games with Jesus when he tempted him, or was there a real battle going on with real freedom and real risk on the line? As a full man, fully free, he must have been ABLE to sin. But if Jesus didn’t sin as the record says, that’s powerful proof that he was also fully divine.
C) What good is knowing this? Much, in that we now know we have a Tri-Personal God who can empathize with our weakness. So the main application is that we should never be shy about revealing our sin to God in prayer. He understands weakness. He knows our condition. So we should be bold about confession and coming to God and trusting in his grace and forgiveness: Heb 4:14-16: “That is why we have a great High Priest who has gone to heaven, Jesus the Son of God. Let us cling to him and never stop trusting him. This High Priest of ours understands our weaknesses, for he faced all of the same temptations we do, yet he did not sin. So let us come boldly to the throne of our gracious God. There we will receive his mercy, and we will find grace to help us when we need it.” NLT Amazing!
The infinite God understands… us! And yet, we need more than empathy. If Jesus could ONLY empathize, he would likely be just like us, a sinner. Then what ability would he have to be our Savior? How could he be our substitute, if he was crucified with his own sins to account for?
As it stands, he remains both perfect and perfectly sympathetic toward our condition. Weakness and temptation are not sin and he experienced a full measure of both. He can relate to our struggles. But due to his perfection, established in actual obedience by his own FREE choices (Heb 5:8,9 – a somewhat troubling passage until we understand Jesus was free and could have sinned, yet didn’t), he can now also carry us.
If it’s examples you need of people who are sinners who press into God and pursue him and live great lives of faith, we have many of those. Jesus didn’t need to come and show us how to respond to God’s grace and be forgiven – except to give us his example of baptism. We already had examples: Abraham, Moses, David, etc. What we needed was not just another example of faith, we needed a Hero! A once and for all sacrifice, the perfect spotless Lamb, who could absorb our stain and carry penitent people to safety in God’s embrace. All people groups have longed for and mythologized idealized Hero figures who are so strong they save many others. The record says among the Jews, in real history, there did come a man who, by his free obedience, became the only true Hero the world has known.