Many Italians emigrated to Argentina because many Italians emigrated. Argentina, like Brazil and the United States could offer economic opportunities not to be found in the old country, but equally importantly, had policies that were open to immigration.
Italian Emigration 1876-1926
Many Italians left Italy in the late 19th and early 20th centuries; it is one of the largest modern emigrations any country has seen (Ireland was another, and Italian and Irish emigré communities became rivals in many places). Argentina was a popular destination, but so were Brazil and the United States, as well as Uruguay and Canada, and numbers of Italians are noted in Venezuela and Peru as well. According to a 1931 paper on emigration between 1876 and 1926, an estimated 8.9 million Italians emigrated to the Americas, 7.6 million to other countries in Europe, 300,000 to Africa, 42,000 to Oceania, and 13,000 to Asia.
After unification in 1861, the Italian economy improved, leading to an increase in population, but the benefits of the economy were not evenly distributed. Generations of subdividing plots had rendered farms too small and inefficient to support the population, especially given poor land management and farming methods, while the phylloxera epidemic wiped out the Italian wine industry starting in the 1870s. An 1884 cholera epidemic could not have helped. In any case, increasing numbers of young Italian men began seeking work abroad, first in France and Switzerland, then in the Americas as transatlantic shipping became more reliable and less expensive.
Labor Demand in the Americas
Argentina was the preferred destination in the 1870s and 1880s, then equally favored with Brazil until the close of the century, when the U.S. became the favored destination until after World War I, when Argentina resumed the crown.
As the great majority of Italian emigrants were economic migrants, it was the availability of work above all that governed their preferred destinations. Argentina was popular at first because of geography; farm laborers could find work in Argentina to earn extra income during the Northern Hemisphere winter. As the economy there boomed— in per capita terms, it was one of the wealthiest countries in the world at the start of the 20th century, thanks to demand for its agricultural products— there was also work to be had in building and railroad construction. Domingo Sarmiento, president of Argentina 1868-1874, encouraged immigration, although he rather wished for more Northern Europeans, even attempting to subsidize them.
In 1890 Argentina suffered a severe economic downturn, the Baring crisis, which also affected its neighbors and the U.S. But Brazil's coffee planters were becoming more aggressive in seeking cheap labor. São Paulo state began to subsidize passage and lodging for recent arrivals, and in the 1880s, coffee plantation owners had begun promoting Brazil heavily as a destination. As such, Brazil began attracting a large proportion of Italian emigrants; indeed, in percentage terms, Italians would become a larger part of the Brazilian population than the Argentinian.
Word of ill-treatment of Italian workers in Brazil led to outrage in Italy, and in 1902 the Prinetti Decree outlaws subsidized emigration to Brazil. This sharply curtailed the number of Italian immigrants to Brazil, and helped swing the numbers to the United States. In contrast to the situation in South America, the U.S. needed cheap labor for its factories, not farms, and some argue that some Italians deemed the life of a factory worker preferable to that of a farm laborer or ranch hand. So the United States absorbed the lion's share of Italians until after World War I, when a series of anti-immigration laws all but closed the country to Southern Europeans (among others).
After World War II, Italian emigration expanded to places like Australia, but improving economic conditions at home would eventually stem the population outflow to more stable levels.