Didn't people from Italy also migrate to Argentina too ?
The Spanish migration to South America in the 1880s must be understood within the context of the general European migration movement during this period. The explanation for why migration flows from the “old world” to the “new” increase so drastically around this time is multi-faceted.
Part I – the communications revolution
The period from the mid-nineteenth century up to the First World War covers what has come to be known (somewhat controversially) as “the first globalisation”. The advent of the efficient and reliable steam engine, used to power both ships and locomotives, meant that transportation costs for passengers and cargo fell dramatically. This in turn had two major consequences. Firstly it meant that the cost of travelling half way across the world decreased drastically, so that ordinary working class people could much more easily afford the process of emigrating in and of itself. Secondly, it meant that produce from the new settler societies could much more easily reach Europe, supplying the demand created by industrialisation and urbanisation.
This also holds true for other technologies beside steam. As an example, the first successful shipment of refrigerated meat from the new world reaches Europe in 1882. Although that particular shipment came from New Zealand, the implications for the now famous Argentine meat industry should be obvious.
As noted above, the second industrial revolution then taking place in continental Europe (although it was still mostly concentrated to central and northern Europe – the Mediterranean countries would begin a process of catch up some time later) held profound ramifications for global trade. Increased raw material consumption in the new factories, as well as increased demand from the rapidly growing urban middle and working classes, together created a booming market in Europe for imports from overseas. This in turn meant that there was a growing demand for labour in much of the new world – including Argentina – pushing wages in these countries upwards. European farmers and industrial labourers could thus earn substantially more by emigrating than they could by remaining in Europe.
Communications between the old and new world also played an important role in facilitating migration. Improved mail and telegraph services, and the resulting greater speed and reliability by which messages and news could reach their destination, meant that there was much greater scope for both advertisement and personal communication across the Atlantic. Knowledge (including advertisement promoting emigration) of the opportunities offered by emigration became much more widespread during this period. Likewise, emigrating did no longer meant cutting ties with home and family, as letters could be exchanged much more inexpensively. The drastically lowered cost of travel also meant that emigration did not necessarily have to be for life. The majority of migrants did indeed settle down in the new world, but it was far from unheard of for people (especially young men) to emigrate for a period of time, before returning home to Europe in order to marry and settle down – perhaps taking over the family farm in the process. The expansion of schooling and increasing literacy rates during this period also contributed to the growing importance of communication. In short, although still a major life choice, improved communication made migration a much less daunting and dramatic step than it had been in earlier time times.
Finally, A range of technological, scientific and social advances meant that western societies managed to break what had become known as the “Malthusian trap”. The Malthusian trap in itself is a major topic for discussion, so I will not go into details here. Suffice to say that European population growth rates exploded through the 19th century. This in turn led to increasing pressure on land, and decreasing returns to labour – almost exactly the opposite of what was happening in the new world. As the rewards for labour and opportunities for social and economic advancement in Europe appeared to be diminishing, the appeal of moving to the settler societies grew.
Thus the ongoing processes of globalisation and communications revolution created both the opportunity to migrates, as well as providing the motivation to do so. The factors combined were enough to entice many Europeans to abandon the old world in order to seek a better life in the new. This is true for Spaniards going to Argentina, as much as it is for Brits, Frenchmen, Germans, Scandinavians and others moving to the Americas, Australia or elsewhere.
Sources and further reading:
Fellman, Susanna, Martin Iversen, Hans Sjögren & Lars Thues (eds.); Creating Nordic Capitalism: The Business History of a Competitive Periphery; Palgrave Macmillan, 2008
Kenwood, A. G. & A. L. Lougheed; The growth of the international economy: 1820-2000; Routledge, 1999
Lewis, William Arthur; Growth and Fluctuations 1870-1913; Allen & Unwin, 1978
Maddison, Angus et al.; The Maddison project database; 2013
Another thing that must be taken into account is the role of Domingo Faustino Sarmiento in the migration process. He was a thinker, military man, teacher and politician most famous for being president between 1868 and 1874 and for being "the father of the classroom" since he was the first to organize and implement a standarized school system. Like many of his peers, people from the argentine intelligentsia (like Juán Bautista Alberdi, ideological father of the definitive 1860 Constitution in which preamble -as in the previous drafts and failed attempts- every man in the world who wants to live in argentine soil is invited, with whom he discussed migration at large) he wanted to populate the then empty Argentina with people from the european countries he admired, namely France and England. Thus he carried out an advertising campaign in Europe, putting up signs inviting people to Argentina, a land ripe with opportunities, and even though they say that at one point people would either go to New York or to Buenos Aires depending which ship sailed first, the crowd that ended up coming consisted in great part of poor spanish and italians, the last thing Sarmiento wanted. This crowd would also bring the seed of labor rights, unions and anarchism, which would become an issue a few decades later.
Between 1871 and 1915 Argentina received 5.000.000 immigrants, to a point where by the turn of the 19th century two thirds of the population of Buenos Aires was foreigner. The vast majority were Spanish and Italian, but there were significant numbers of French, English, Polish, Russian, Syrians, Armenians, Germans and Welsh. A very minor detail which is usually said is that some of them looked for lands with more opportunities that still reminded them of home, and that is why there is a big german settlement in Bariloche, amidst alp like mountains, and a welsh one in harsh Gaiman, Chubut.
While not exactly answering OP's question, I'd add that the influence of Italian immigration cannot be overstated. While Argentina today (but mostly Buenos Aires and the surrounding or further away but still similar places) is very multicultural, Argentines (and again, especially people for Buenos Aires) are basically Italian since their influx shaped forever the Argentine idiosyncracy. after 1900 it is said that the accent changed drastically from a very spanish like demeanor to the fast paced, singsong italian way of speaking, the slang began to be mainly bastardized italian (which still is to this day in a city where people talk with high doses of slang), the exaggerated hand movements while talking, the warmth and touchy-feeliness with friends, the concept of family, the food, all of this is a direct heritage from Italian immigration. And while traces of other countries can definitely be found, nothing is as overwhelming as the Italian.