I recently started reading about the First (and second) Mexican empires and had this question in the back of my mind the whole time. Why were the Mexicans so hell bent on having a European as monarch? And why did Ferdinand decline the offer of Mexico becoming a Commonwealth?
Edit: I'll expand the question in hopes someone will see it.
The injection of a European royal in the second empire makes sence to me since Napoleon III was looking to push his influence in the Americas and having a member of his blood line in Mexico gave him a in and a puppet from which to expand his influence. But for the first empire, I would assume (probably incorrectly) that the recent independence would fuel a more nationalistic idea of a Mexican being crowned Emperor like how Iturbide was eventually crowned.
For one thing, you have to understand that the separatist movement that succeeded in Mexico was an essentially conservative one (conservative with a lower case c, not upper case Conservatism as it would exist in Latin America in the following decades). Absolutist monarch Fernando VII had been temporarily obliged to accept a constitution which was essentially liberal (in the Spanish sense) in 1820 after 'Riego's Revolution' (an uprising of liberal military officers in Spain).
Liberalism in Spain meant two things. In social issues, like the role of the Church and potentially even slavery, it was usually very modernizing. In economic issues, it meant a strengthening of metropolitan economic controls over Spain's overseas colonies. This is exemplified in the Liberal constitution of the 1830s.
So when Iturbide and the other pro-status quo officers rebelled they were, to cop a phrase from Lampedusa's The Leopard, changing everything so that nothing changes. New Spain (later Mexico) was, after all, a vice royalty (virreinato), so the idea was to proceed towards independence to defend their interests, both economic and in social matters, against peninsular liberals but without significantly altering the established order. In particular they had in mind the radical independence movements of the previous decade which had successfully energized popular sectors who were normally not active players in politics.
Attracting a European monarch solved two potential issues. It would help establish a new regime which would perpetuate the status quo in socio-economic issues, backed by all the legitimacy that an old European aristocratic house could provide. It would also potentially defuse the situation with Spain, such as if a Bourbon monarch sat on the Mexican throne. Brazil, for example, became an empire with a cadet branch of the Portuguese royal family from the 1820s up until the 1880s. Mexican elites were looking for something similar. When that failed, they tried to invent an empire. Didn't turn out so well.