Why doesn't hallucination, common burial, legend, and gullibility explain the rise of Christianity (rather than the Resurrection)? How is this wrong?
Two incidents can give a partial explication. I am limiting myself to Biblical references only as one can go one and on with this subject matter. And mere opinions do not carry no proofs here. One believes or one simply does not believe.
If this was not of God, it would have been doomed to failure. A Pharisee named Gamaliel warned the Sanhedrin that “if their purpose or activity is of human origin, it will fail. But if it is from God, you will not be able to stop these men; you will only find yourselves fighting against God.”
25 Then someone came and said, “Look! The men you put in jail are standing in the temple courts teaching the people.” 26 At that, the captain went with his officers and brought the apostles. They did not use force, because they feared that the people would stone them.
27 The apostles were brought in and made to appear before the Sanhedrin to be questioned by the high priest. 28 “We gave you strict orders not to teach in this name,” he said. “Yet you have filled Jerusalem with your teaching and are determined to make us guilty of this man’s blood.”
29 Peter and the other apostles replied: “We must obey God rather than human beings! 30 The God of our ancestors raised Jesus from the dead—whom you killed by hanging him on a cross. 31 God exalted him to his own right hand as Prince and Savior that he might bring Israel to repentance and forgive their sins. 32 We are witnesses of these things, and so is the Holy Spirit, whom God has given to those who obey him.”
33 When they heard this, they were furious and wanted to put them to death. 34 But a Pharisee named Gamaliel, a teacher of the law, who was honored by all the people, stood up in the Sanhedrin and ordered that the men be put outside for a little while. 35 Then he addressed the Sanhedrin: “Men of Israel, consider carefully what you intend to do to these men. 36 Some time ago Theudas appeared, claiming to be somebody, and about four hundred men rallied to him. He was killed, all his followers were dispersed, and it all came to nothing. 37 After him, Judas the Galilean appeared in the days of the census and led a band of people in revolt. He too was killed, and all his followers were scattered. 38 Therefore, in the present case I advise you: Leave these men alone! Let them go! For if their purpose or activity is of human origin, it will fail. 39 But if it is from God, you will not be able to stop these men; you will only find yourselves fighting against God.”
40 His speech persuaded them. They called the apostles in and had them flogged. Then they ordered them not to speak in the name of Jesus, and let them go.
41 The apostles left the Sanhedrin, rejoicing because they had been counted worthy of suffering disgrace for the Name. 42 Day after day, in the temple courts and from house to house, they never stopped teaching and proclaiming the good news that Jesus is the Messiah. - Acts 5:25-41
Another factor that helped spread the Word was the abundance of miracles operated by the Apostles themselves and the descendants in the Early Church.
Peter’s Miraculous Escape From Prison
12 It was about this time that King Herod arrested some who belonged to the church, intending to persecute them. 2 He had James, the brother of John, put to death with the sword. 3 When he saw that this met with approval among the Jews, he proceeded to seize Peter also. This happened during the Festival of Unleavened Bread. 4 After arresting him, he put him in prison, handing him over to be guarded by four squads of four soldiers each. Herod intended to bring him out for public trial after the Passover.
5 So Peter was kept in prison, but the church was earnestly praying to God for him.
6 The night before Herod was to bring him to trial, Peter was sleeping between two soldiers, bound with two chains, and sentries stood guard at the entrance. 7 Suddenly an angel of the Lord appeared and a light shone in the cell. He struck Peter on the side and woke him up. “Quick, get up!” he said, and the chains fell off Peter’s wrists.
8 Then the angel said to him, “Put on your clothes and sandals.” And Peter did so. “Wrap your cloak around you and follow me,” the angel told him. 9 Peter followed him out of the prison, but he had no idea that what the angel was doing was really happening; he thought he was seeing a vision. 10 They passed the first and second guards and came to the iron gate leading to the city. It opened for them by itself, and they went through it. When they had walked the length of one street, suddenly the angel left him.
11 Then Peter came to himself and said, “Now I know without a doubt that the Lord has sent his angel and rescued me from Herod’s clutches and from everything the Jewish people were hoping would happen.” - Acts 12:1-11
Certainly the miracles of physical healing won many over to the teachings of Jesus.
The Apostles Heal Many
12 The apostles performed many signs and wonders among the people. And all the believers used to meet together in Solomon’s Colonnade. 13 No one else dared join them, even though they were highly regarded by the people. 14 Nevertheless, more and more men and women believed in the Lord and were added to their number. 15 As a result, people brought the sick into the streets and laid them on beds and mats so that at least Peter’s shadow might fall on some of them as he passed by. 16 Crowds gathered also from the towns around Jerusalem, bringing their sick and those tormented by impure spirits, and all of them were healed. - Acts 5:12-16
And finally, one last Scriptural example, as I could add many more. God can employ many means to spread his message of salvation.
11 God did extraordinary miracles through Paul, 12 so that even handkerchiefs and aprons that had touched him were taken to the sick, and their illnesses were cured and the evil spirits left them. - Acts 19:11-12
Of interest may be the following article: Spread of Christianity.