Is poverty rightly measured internationally? According to the World Bank, Argentina has 3.63% or people living in poverty. As a subjective assessment of someone living there, this is completely ridiculous. Rates measured by Argentine government and Argentine private institutions set it around 32% to 34%, and they are widely accepted as representative figures of Argentina's today reality. 

As far as I understand, the definition used by the World Bank to define a person as poor says someone is poor when he earns less than US\$ 3.1 a day. That makes US\$ 90.30 dollars a month. Now I understand that the living costs are different in different countries, but how could they reach a figure of US\$ 90.30 a month to cover basic needs? How can a person with US\$ 90.30 dollars a month cover basic needs anywhere?
This measure of poverty depends on your definition of basic needs and local prices. Argentina is a good example for how local prices matter. It is widely accepted that official price and inflation statistics published by the Argentinian government are cooked and inflation rates in the last few years are have been substantially bigger than official numbers suggest. I assume that the world bank has to rely on those statistics and it is therefore likely that its  estimates of poverty in Argentina are too low, simply because the price level adjustment is not done with good data.

Alberto Cavallo has a nice paper showing the discrepancies of official statistics with other measures of Inflation in Argentina, see here.

Living on 90$ a month is obviously not nice, but around the world many people do. This measure is intended to document the extent of  extreme poverty in developing countries, i.e. the circumstances where you are literally close to starving. Many more developed countries use a much higher poverty line in their domestic statistics. The world bank as an international body publishes statistics on development that are internationally comparable, and hence uses the same threshold for each country.

The World Bank's extreme poverty line used to be much lower - I believe it started out at 1$ per day around 1990. You can read up on the intention of publishing such a statistic, and how the threshold is chosen in this interesting blog post by a World Bank economist.