Most soldiers and pilgrims wanted to leave Antioch and continue the march south to Jerusalem because they wished to fulfill their vows and to see the very site — Calvary Hill — where Christ was crucified. They believed they could reach Jerusalem in about ten days time. But the princes thought otherwise: the army needed to rest up and, since there was still a chronic shortage of food, horses and other materials, they needed to find someplace where they would be resupplied. Lucky for the crusaders, Genoese merchants arrived in Antioch in early July with food and other supplies. Still, it would take time for them to prepare for their march south and the princes were not prepared to take that risk in the heat of summer. Then, there was the question of who would govern and garrison Antioch. Antioch rightfully belonged to the Byzantines, but greed and ambition got in the way, breaking the unity in the crusading army, particularly between Bohemond and Raymond of Toulouse.
Bohemond demanded that Antioch be handed over to him. After all, he argued, he had engineered the city’s downfall and it was due to his strategy and skill as a warrior that the army was able to crush Kerbogha’s forces. So, he had every right to govern the city. Besides, Bohemond was already acting as if the principality of Antioch was his: in early July, he opened the market to Genoese merchants, allowing them to settle and conduct business.
Count Raymond took great exception to Bohemond’s haughty behavior. Even though Raymond had not sworn the oath of allegiance to Alexius, he demanded that Antioch be handed over to Alexius as promised. It would be wrong to suggest that Raymond’s motives were entirely pure. Like his cohorts, he desired to obtain an eastern lordship for himself. More than anything, though, Raymond wanted to be recognized as the leader of the Crusade. However, Bohemond stood in his way and Raymond highly resented him for that. It is quite possible that Raymond was jealous of Bohemond’s strength and military prowess.
Raymond was not alone: he had a faithful ally in Bishop Adhemar — the two men had been close friends since the time before Pope Urban preached at Clermont in November 1095. Adhemar strongly advised Bohemond and the other princes to cede Antioch to the Emperor. Adhemar saw the need to maintain good relations with Byzantium. Alexius had proven to be a valuable and reliable ally; he had — until the crusaders reached Antioch — helped keep the Muslim threat at bay. Moreover, Adhemar, like Pope Urban, believed that the Crusade had served as a bridge, uniting the eastern most part of Christendom — meaning the Greek Orthodox Church — with the Latin West. For those reasons, he did not want to jeopardize their good relations with Alexius.
The other princess — Godfrey, Tancred, Robert of Normandy and Robert of Flanders — were, themselves hesitant to break their oath to Alexius. Yet, they did not want to get in the way of Bohemond’s ruthless ambitions. However, given that Alexius had not arrived — it was quite possible the crusaders did not yet know about Stephen’s interview with Alexius at Philomelium — and that his commander, Tatikios abandoned them halfway through the siege, they were not so sure they wanted to hand over Antioch to Alexius. Someone had to govern and garrison Antioch, though. The crusaders could not leave the city without a leader. If they did so, Antioch would be recaptured by the Turks and those long, agonizing months of suffering and intense siege warfare would have been for not.
Probably on Adhemar’s advice, Hugh of Vermandois departed for Constantinople to explain the situation to Alexius.
Asbridge, Thomas. The Crusades: The Authoritative History of The War For The Holy Land. Ecco; New York, 2011.
Runciman, Steven. A History of the Crusades: The First Crusade. Vol.1. Cambridge; Cambridge University Press, 1951.