What might explain why the Dutch believed that they had more of a claim on New Amsterdam than the British?

The Dutch were the first settlement of New Amsterdam in New York City. In 1906, Henry Hudson was an English sea captain that worked for Dutch merchants and was trying to find a Northwest passage to Asia. However, he ended up exploring the Atlantic seaboard of North America. He came up to an island of Manhattan and 150 miles North and today the Hudson river was named after him. The Dutch were first to start trading post called fort Nassau, later fort orange near modern day Albany. The post had only a tiny Dutch population of some 50 traders and soldiers, but Dutch ships sailed regularly up the Hudson to collect furs and more Dutch expeditions explored the area, which became the colony of New Netherland, run by the Dutch West India Company. In 1625 the company founded New Amsterdam at the southern tip of Manhattan Island as the colony’s capital and seat of government, with a fort to protect it and guard the harbour and the precious fur cargoes against English or French raids. Peter Minuit of the Dutch West India Company, who was in charge from 1626, decided to buy Manhattan Island from a group of local Indians for goods worth 60 Dutch guilders, which later legend valued at US$24. It has been rated the best real estate deal in history.