Why did Mexico's first attempt to win independence fail?

Answer 1

Because at the time (1562), Spain was at the height of its dominance over several overseas territories in the Americas; also the conspirators didn't have enough supporters to form an effective rebellion.

In 1562, the encomienda system (effectively, a feudal system) was changed so that when the encomendero died, all his possessions and subjects would be handed over to the government, instead of the encomendero's family. This enraged wealthy landlords such as Martin Cortes (1523-1595), who started a poorly-backed conspiracy to secede from Spain. He and all his co-conspirators were captured however, and some were executed for treason. Cortes himself was pardoned, dying in Spain from natural causes around 1595 (although some accounts state that he died around 1574).