Final answer:
The Spanish sought to convert native peoples to Catholicism as part of a socio-religious model granting them labor control and religious dominance, influenced by the Spanish Inquisition and the Reconquista ideologies.
Step-by-step explanation:
The Spanish were eager to convert people to Catholicism for several reasons, one being the reciprocal relationship which they believed entitled them to control native labor in exchange for bringing Catholicism to the New World. Their socio-religious model assumed that native peoples would willingly become beasts of burden for the Spanish, while acquiring the 'right' religious beliefs. This exploitation, however, met with resistance as native people often retained their religion or blended Catholicism with their own beliefs.
The work of secular clergy and missionaries like Dominican friar Bartolome de las Casas, who sought to educate and understand the native populations, popularized Catholicism. Yet Spanish priests and missionaries also faced resistance, exemplified in the Pueblo revolt, when natives were compelled to abandon their traditions entirely. This resulted in tensions that combined with other hardships, leading to the Pueblo expelling the Spanish to return to their native ways.
Furthermore, the Spanish Inquisition and the Reconquista influenced the Spanish to extend their religious conquest to the New World. The Spanish Crown held an iron grip on religious matters after the Reconquista, viewing the extension of Catholicism into their colonies as a duty of their newfound religious identity. Consequently, with the military conquest, the religious conversion was also intrinsically carried out.
In summary, the Spanish were driven by a complex mix of duty, the pursuit of control over labor, and the consolidation of their Christian identity, which was fueled by the ideologies born from events like the Reconquista and the Spanish Inquisition.