Explaining why something didn't happen is difficult for a variety of reasons, but we can try. First, we know that Argentina was wealthy and successful in the early 20th century: they were a top 10 state by GDP per capita in that time and experienced solid economic growth until the 1970s, when things started to peter out.

One thing you point out is that Argentina has historically been an agricultural super power. It has, for example, been a leader in wheat and beef exports for a long time. However, an issue they ran into was industrialization. In the late 19th century, early 20th century the countries that were or would become great powers were leaders in industry. This includes the US, UK, Germany, Japan, etc. Argentina did not successfully industrialize to the extent that these other states had, which was an issue especially as war, power projection, and trade development became increasingly industrialized. Further, while Argentina has access to abundant natural resources, it has relatively limited access to domestic iron, coal, and oil, which were the drivers of the industrial age.

Another issue Argentina had was its location. Look at the US, it has long borders on the Atlantic and Pacific, and has relatively short routes to Europe and East Asia. This played a hugely beneficial role in the development of US trade as it has ready access to the two most influential foreign markets in the world (not to mention a preeminent place in New World trade). Argentina, meanwhile, is located at the south of the south, putting it out of the way for global trade. Further, Chile basically precluded any chance Argentina had at having a Pacific port, which made trade with Pacific states more difficult as Argentine ships had to traverse Cape Horn or the Panama Canal to get to East Asia.

Finally, while Argentina is large and was wealthy at the time, their geopolitical position is somewhat perilous. It is located on a fairly crowded continent, next to a much larger neighbor (Brazil). The US, as a contrast, had basically settled its domestic security issues by the mid-19th century as it was much larger and stronger than Mexico and relations with Britain (and thus Canada) improved. Also, the Monroe Doctrine basically precluded the re-entrance of European great powers to the Americas and those that remained (GB, France, Netherlands, Denmark, and Spain) generally had small holdings that were non-threatening to the US.

There are surely other reasons that precluded Argentina's development. We should also acknowledge that development is difficult and not guaranteed, and further that the Middle Income Trap is real and hard to escape.

Overall, though, the main reasons Argentina stagnated have to do with its location and failure to industrialize to the extent that other states had.

See The Crisis of Argentine Capitalism by Paul Lewis for more.