Why might the Spanish have targeted the Aztecs religious house of worship first?

So they can convert them to Christianity and show them they were worshiping false gods

The history of the Catholic Church in Mexico dates from the period of the Spanish conquest (1519–21) and has continued as an institution in Mexico into the twenty-first century. Catholicism is one of the two major legacies from the Spanish colonial era, the other being Spanish as the nation's language. The Catholic Church was a privileged institution until the mid nineteenth century. It was the sole permissible church in the colonial era and into the early Mexican Republic, following independence in 1821. Following independence, it involved itself directly in politics, including in matters that did not specifically involve the Church