Spanish possessions were more solidly held. Portuguese control over Brazil must have seemed more tenuous (at first glance). Portuguese holdings in Asia at least, were pretty tenuous, and their lower population would have made them more vulnerable.
But I do get mistified as to why the Dutch didn't just go to Argentina instead. I hear from unreliable sources that the weather is more amenable.
Argentina, or rather what became Argentina was a very peripheral territory of seemingly little value. Northeastern Brazil, most notably Pernambuco and to a lesser extent Bahia were the world's leading sugar-producing regions and the Netherlands was Europe's primary sugar-refining and distribution hub. After the end of the 1609-1621 truce the Dutch were effectively embargoed from trading Portuguese sugar and in response Dutch investors established the West India Company in 1621. In 1624 they were even able to capture Salvador, the capital of the colony.
It was not without reason that the Dutch paid no attention to southern Brazil and the Rio de la Plata. Even as late as 1800, the captaincy of São Paulo accounted for less than 5% of all Brazilian trade with Europe and even Rio de Janeiro was a backwater until after 1700 when gold was discovered there. Southern Brazil and the Plata River basin provided little trade except in the export of hides and smuggling of silver from Upper Peru with some clandestine trade in slaves. However, this trade was very small when compared with the other colonial entrepots.
Wihout the Union, the Dutch are likely happy enough to trade with the Portuguese and vice versa. The beginning of the troubles between Portugal and the Netherlands only began in 1595, when Philip II had 400 Dutch ships seized in Iberian ports. This was followed by the closing of Portuguese ports to Dutch traders in 1596. Before 1580, Portuguese shipping was indadequate to handle the sugar cargo that English and Dutch ships were even allowed to sail to Brazil to buy sugar directly.
The Dutch stadtholder were forced by the embargo to send exploratory missions to what is today Suriname looking for salt as they traditionally bought Portuguese salt to preserve herring. This was followed by sending ships the East Indies, culminating in the creation of the VOC in 1602. In February 1603, the VOC seized a Portuguese carrack, once they sold its goods, the value of the company doubled. By 1604, the Dutch were able to launch their first attack on Portuguese Malacca (unsuccessful at that time). However, in 1605 they captured Amboyna in the Moluccas, this was followed by the Spanish fort at Ternate in 1610. Most importantly, they were able to establish Batavia as their base in 1619.
The Dutch were unlike the Portuguese exclusively concerned with profit and their colonial exploration only came out of necessity. It took a few decades for the VOC to become profitable, while the WIC was an unprofitable venture, with the company going bankrupt.
Without a state of war between the Portuguese and Dutch, they are likely content to use the Portuguese as middlemen, particularly as it was a more advantageous relationship to the Dutch. The Portuguese had the expense of sending men and armed ships to the East along with building and maintaining fortresses.
After the 1550s, the bulk of profits from the Eastern trade were going to the Dutch merchants, as their ships dominated trade with Portugal and few Portuguese ships ventured north of Spain. Dutch merchants bought spices, textiles and other Eastern goods along with sugar from the Portuguese and redistributed these goods throughout Germany, the Baltic and the rest of northern Europe. At the same time, they sold northern European manufactured goods to the Portuguese. Portuguese traders were largely limited to trading with Spain, France and the Mediterranean, and this was eclipsed by the trade with Antwerp and later Amsterdam.
From its founding until the 1609 truce, the VOC was largely an instrument of war, rather than of commerce and "the subsidies it received from the federal government of the Netherlands were not nearly enough to cover its military expenses and, after the first twenty years of operation, the debt accumulated by the VOC nearly equalled the capital outlay of the company" (Emmer, First Global War). Around one-half of the company's profits between 1602 and 1609 came from piracy (1 million guilders per year).