In North America, we have the continent-spanning countries of Canada, the United States and Mexico, which each consist of a number of provinces/states, unified under a federal government, and a significant number of which could easily be countries in their own right.
However, in Central and South America, we instead find a large number of individual countries instead. Why did these regions seek individual independence, rather than becoming federalized countries like the regions in the North did?
Well, the reason is primarily because of how independence came about. Also, you shouldn't really exclude Mexico from the rest of Spanish America, as it too was a huge part of this process, and shows there were some moves towards larger nations.
Anyway, independence was begun when Spain fell to France in the Napoleonic Wars. Napoleon placed his brother on the throne, and Spain (including overseas territories) rejected this, beginning the Peninsular Wars. Following the appointment of Joseph Bonaparte to King of Spain, there were several pretenders to the throne (called juntas) representing different regions. Without a central body to unite them they didn't recognise the authority of one another, especially those who claimed representation of Spanish America. The juntas proved ineffective and did nothing to keep the Spanish empire united.
Realising this, the juntas established a central body for the juntas. This central junta established that Spain would be divided up into it's historical kingdoms, and Spanish America would be divided into 10 kingdoms (roughly equivalent to the modern nations). However, this proved unpopular too. Major cities that were previously considered capital cities had their previous country been annexed into a larger territory and received little to no representation in this central body. This triggered rebellions in these areas and their local authorities were soon defeated. But it was also the effective establishment of several, not one, independent Spanish American nations.
France then essentially forced this central body into hiding, and it was dissolved. The Spanish then attempted to create a new, more representative government-in-exile, but Spanish America saw no reason to recognise legitimacy in this government that could easily be dismantled any day by the French. The Spanish American nations set about trying to seek their own, local independence, from the French.
It was the lack of central authority that triggered the arising of several nation states in Spanish America. But coupled with that is the fact that there was no unifying identity to keep the people together. Before the French had really gotten their full strength in Spain, Spanish Americans were also just Spanish, they too were fighting the French. Then it became a fact that they were all Spanish Americans, but this too failed.
The only successful tactic to remove them from the Napoleonic Empire was to fight as regional organisations. Also, as regional organisations they could seek independence from each other if they felt worthy. If Spanish America became independent as one nation, there was the question of whether some regions would stay subservient to others as they had been prior to independence.
The United States and Canada had central authorities that united them (in the federal government and Westminster parliament). Also, they were not continent spanning when formed, they grew into continent spanning nations.
hi! you may be interested in this section of the FAQ. Despite the title, the larger North American countries are included in many of the discussions.