Why did the twelve apostles stay in Jerusalem when the other believers left?
The twelve apostles stayed in Jerusalem to present the message to the nation of Israel, hoping Israel would still accept their King so Christ could come and set up the Kingdom. They were to stay and present this to Israel, while the other believers were scattered.
The teaching explains that the twelve apostles were not to leave Jerusalem, but all the rest of the believers had. They were to stay and present the offer of the King and the Kingdom to the nation of Israel, in hopes that Israel would still accept their King, and Christ could have come and set up the Kingdom. The disciples understood that once they had the King and the Kingdom, they knew the Old Testament prophecies. Zechariah chapter 8 was cited, where ten men of all nations shall take hold of the skirt of him that is a Jew, saying, 'We will go with you,' because they know that God is with you in the person of the King. Meanwhile, the other believers, after Stephen's death, were scattered from Jerusalem and migrated up to Antioch, north of Palestine, in the area of Lebanon today, preaching to Jews only at first. But some men of Cyprus and Cyrene, when they came to Antioch, spake unto the Grecians preaching the Lord Jesus.