At Foreign Policy Joshua Keating writes about how in retrospect the recognition of a Palestinian state by Latin American governments should be seen in the context of a careful Palestinian strategy:
At the time, the moves were mostly viewed in terms of what they said about Latin American politics, showing countries plotting a course independently of the United States with strong influence from non-aligned Brazil.
In the context of Palestinian negotiations with Israel, the support of say, Paraguay, didn't seem all that consequential. But with international recognition of Palestine very much on the world's agenda this week, the Palestinian overtures to South America make a lot more sense. Looking at the map above, Palestine is currently recognized not only by all four BRICs, by nearly the entirety of the developing world with the exception of a few pariah states like Eritrea and Burma and some pro-American bastions like Colombia and newly independent South Sudan.
I don't necessarily disagree, but I do think the question of why Latin American governments chose to do so should still be connected to Brazil's prestige. If, for example, Venezuela had attempted to lead the way, then we might not have seen that string of announcements (on that point, Hugo Chávez wrote a letter to the UN claiming among other things that anti-Semitism is solely a western phenomenon). Probing that question of why would be a good research topic.