Final answer:
The extended rivalry between crusade leaders back into Europe was largely driven by political ambitions as they sought to build up nation-states and secure power over their rivals.
Step-by-step explanation:
The rivalry among crusade leaders that extended back into Europe was ultimately fueled by political ambitions. Post-crusades, European leaders and aristocrats shifted their focus towards nation-building and engaged in conflict with rival dynasties to consolidate power and expand their territories.
The crusading spirit was manipulated to serve the geopolitical interests of kings and monarchs who often sought the papacy's endorsement for their military campaigns. This competitive environment led them to utilize the ideology of crusades to legitimize their political and territorial disputes, thereby extending the rivalry born out of crusading spirit back into European politics.