Already answered multiple times, as found in the wiki.

Essentially, there were profound differences on the continent enforced by the autonomous natures of the Virreinatos (Viceroyalties) and the lower administrative units such as the Capitancia General (General Captaincy) and the Real Audencia (Royal Audience). The continent was divided into three Virreinatos when the independence wars broke out and their respective campaigns were led separately with Simón Bolívar in the north in the Virreinato de Nueva Granada and José de San Martín in the south, in the Virreinato de Río de Plata. As such, the high levels of autonomy, huge distances of land, and vast regional differences prevented a strong continental movement from forming.

An important historical note, Bolívar did envision a united South American republic and expressed his interest in forming one during his famous meeting with San Martín. The latter informed the former that while the Capitancia General de Chile was willing to enter, the administration at Buenos Aires was not so.

Essentially, Spanish South America was covers a huge expanse with scattered coastal population centers surrounded a vast hinterland populated still in most parts by various indigenous people with different customs and languages. The population centers (which are now the capital cities of the South American nations such Quito, Bogota, Lima, Buenos Aires, etc) rivaled each other in size, prestige and economic activity, and there was no single one that had achieved primacy or gained more importance than the others. Since the elites of these cities were in constant competition with each other, there was no reason for any single city (and its surrounding environs) to defer their authority, political influence, to another, especially if they were essentially equivalent in status.

It is helpful if you think of a hypothetical analogy, such as how Philly will never defer to Boston and vice versa, but both cities may potentially defer to NYC, (but problem was, there was no NYC at the time). And given the vast separation between these cities, they each developed their own unique cultural identity and distinctiveness, enough so at least, for the local political elites declare their local area independent of any centralized South American authority. Therefore, the bottom line is that, it was a lack of unity amongst the different south American people after the unifying forces (namely, Simon Bolivar and Jose the San Martin) had left the stage.