Why did the natives in North America build large ships to travel the oceans?
They were mostly just too late to the party.
The Europeans weren't building them for very long before they crossed the Atlantic. Sophisticated European shipbuilding really didn't take off until the early 1400s by the Portuguese. And as sailing along Africa turned out to be quite profitable, this continued to fuel more innovation. It was fewer than 200 years later that the most advanced and powerful civilizations in the Americas were completely subjugated by the Spaniards.
So basically, though ships of this nature did not exist in the Americas before the arrival of the Europeans, they didn't exist in Europe too much earlier either. These civilizations were completely isolated before then, so it is not surprising that their shipbuilding prowess was not advancing in lockstep.