In the mid-19th century a large wave of immigration started to arrive in Argentina due to new Constitutional policies that encouraged immigration, and issues in the countries the immigrants came from such as wars, poverty, hunger, famines, pursuit of a better life, among other reasons. The main immigration sources were from Europe, the countries from the Near and Middle East, Russia and Japan. Eventually Argentina became the second country that received the most immigrants in the world, only second to the United States.
Therefore, most Argentines are of European descent, and are either descendants of colonial-era settlers and/or of the 19th and 20th century immigrants from Europe, with about 86% of the population being of ethnic European descent.
The most common ethnic groups are Italian and Spanish (including Galicians and Basques). It is estimated that up to 25 million Argentines, up to 60% of the total population, have Italian ancestry, wholly or in part.
So, basically, there are a ton of white people, but they are not all that there is to Argentina. In my experience, it depends a lot on which part of Argentina you are visiting, and on whether you are in an affluent neighborhood or not.
Then again, who cares?