They wanted to defend the fur trade. Here's an explanation from Wikipedia:
New Amsterdam (Dutch: Nieuw Amsterdam, pronounced [ˌniʋɑmstərˈdɑm] or [ˌniuˈʔɑms-]) was a 17th-century Dutch settlement established at the southern tip of Manhattan Island that served as the seat of the colonial government in New Netherland. The factorij became a settlement outside Fort Amsterdam. The fort was situated on the strategic southern tip of the island of Manhattan and was meant to defend the fur trade operations of the Dutch West India Company in the North River (Hudson River). In 1624, it became a provincial extension of the Dutch Republic and was designated as the capital of the province in 1625.