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After Simon Bolivar drove out the Spanish in South America, he was briefly president of much of Spanish-speaking South America. His vision was for it to be a united country. Other political factions felt differently.
Further north, Mexico and Central America were briefly united after independence -- they were all administered as part of New Spain by the Spanish. Then, modern-day Central America was united as one country for a bit before breaking up into different countries like it is today.
The reasons were different from place to place, but generally speaking, despite having the same language and some cultural similarities, there were too many different political factions, different local leaders who wanted power and not enough of a sense of national unity for these big federations to be workable in the long run.