It has nothing to do with whether or not Jesus did it. It is simply because it cannot be done because by and large most claims of healing are fake.
You can not disprove the real because there is fake out there. There are fake christians too! But there is also the real!
One of the definitions of "authority" is:
"a power or right delegated or given; authorization"
Notice that the Jewish chief priests sent out Saul (later to be known as the apostle Paul) to arrest Christians, so Saul was acting on their authority:
Acts 26:10: "And that is just what I [Saul] did in Jerusalem. On the authority of the chief priests I put many of the saints in prison, and when they were put to death, I cast my vote against them."
Saul wasn't acting in his own authority, but instead he was acting in the authority of a higher power (the chief priests) who had sent him on a mission.
When Jesus sent out the twelve apostles to operate in His ministry of preaching the Gospel and healing the sick, He delegated to them the power and authority that they needed (Luke 9:1). Therefore, they were operating in His authority. When He sent out the 72 believers to operate in His ministry of preaching the Gospel and healing the sick, He delegated to them the task of healing the sick and said that He had given them authority over the enemy (Luke 10:1-3, 9, 19). Therefore, they were operating in His authority. When He sent out the Church to operate in His ministry of preaching the Gospel and healing the sick, He was delegating to us these tasks (Matthew 28:18-20, Mark 16:15-18). Therefore, we do these things in His authority:
Luke 9:1: "When Jesus had called the Twelve together, he gave them power and authority to drive out all demons and to cure diseases,"
Luke 10:1: "After this the Lord appointed seventy-two others and sent them two by two ahead of him to every town and place where he was about to go."
Luke 10:2: "He told them, "The harvest is plentiful, but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field."
Luke 10:3: "Go! I am sending you out like lambs among wolves." ...
Luke 10:9: "Heal the sick who are there and tell them, 'The kingdom of God is near you.'" ...
Luke 10:19: "I have given you authority to trample on snakes and scorpions and to overcome all the power of the enemy; nothing will harm you."
Matthew 28:18: "Then Jesus came to them and said, "All authority in heaven and on earth has been given to me."
Matthew 28:19: "Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,"
Matthew 28:20: "and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.""
Mark 16:15: "He [Jesus] said to them, "Go into all the world and preach the good news to all creation."
Mark 16:16: "Whoever believes and is baptized will be saved, but whoever does not believe will be condemned."
Mark 16:17: "And these signs will accompany those who believe: In my name they will drive out demons; they will speak in new tongues;"
Mark 16:18: "they will pick up snakes with their hands; and when they drink deadly poison, it will not hurt them at all; they will place their hands on sick people, and they will get well.""
When we heal the sick and cast out demons, we're not acting in our own authority, but instead we're acting in the authority of a higher power (Jesus) who sent us out to do these things.
Here's another way to look at it. One of the definitions of "in the name of" is:
"b. by the authority of"
When we're operating in Jesus' evangelism and healing ministry (which He delegated to us) then we're acting "in His Name," which means that we're acting in His authority:
Acts 3:6: "Then Peter said, "Silver or gold I do not have, but what I have I give you. In the name of Jesus Christ of Nazareth, walk."" ...
Acts 4:6: "Annas the high priest was there, and so were Caiaphas, John, Alexander and the other men of the high priest's family."
Acts 4:7: "They had Peter and John brought before them and began to question them: "By what power or what name [authority] did you do this?""
So when we're sent out by a higher power to do something, and we do it "in the name of" that higher power, this means that we're doing it in the authority of that higher power. For example, when a police officer says, "Stop in the name of the law," he has the full authority of the government backing him up. Since Jesus commissioned us to preach the Gospel, heal the sick, and cast out demons, we do these things in His authority. When we do these things "in His Name," this means that we have His full authority backing us up.
