Why did Native Americans not object when Columbus claimed territory for Spain?

Answer 1

Objecting implies understanding the procedure. The Native Americans did not understand what "land claiming" is. Additionally, Columbus claimed the land in the Carribean in Spanish, which most Native Americans did not understand.

The concept of exclusive property ownership, which is dominant in most settled societies (and especially in Europe both then and now as well as the current USA), is based on the following idea. Somebody acquires a piece of land, either by purchase, inheritance, or conquest, and then he is the only person who can access the land. If others wish to access the land, they must get the permission of the owner. The owner has free reign over this property and nobody save a national government can expropriate the land from him. It follows naturally that someone with the view that all property is subject to exclusive property ownership would see "unowned property" in a desirable location and then claim it since this would then provide the benefits of exclusive ownership.

The Taino and Arawak Tribes of the Carribean had mutual land ownership, which means that various tribes would have overlapping territorial regions. Since no parcel of land pertained to only one tribe, the various tribes that controlled a given area moved around and settled at will. However, none could modify the land or eject someone who was within the shared area. Additionally, while the borders between exclusive properties are quite clear, the borders between mutually owned lands are much fuzzier.

This is why the idea that someone (Columbus) would assert that the land was exclusively his made no sense. He was not one of the tribes that had mutual ownership before, but there was no reason that Columbus' tribe (i.e. the expedition) could not share the land with the tribes who were already established there, provided that they behaved well.