Why are there mountains along the west coast of North and South America

On the West coast of North America, the coast ranges and the coastal plain form the margin. Most of the land is made of terranes that have been accreted onto the margin. In the north, the insular belt is an accreted terrane, forming the margin. This belt extends from the Wrangellia Terrane in Alaska to the Chilliwack group of Canada.

A rupture in Rodinia 750 million years ago formed a passive margin in the eastern Pacific Northwest. The breakup of Pangea 200 million years ago began the westward movement of the North American plate, creating an active margin on the western continent. As the continent drifted West, terranes were accreted onto the west coast. The timing of the accretion of the insular belt is uncertain, although the closure did not occur until at least 115 million years ago. Other Mesozoic terranes that accreted onto the continent include the Klamath Mountains, the Sierra Nevada, and the Guerrero super-terrane of western Mexico. 80 to 90 million years ago the subducting Farallon plate split and formed the Kula Plate to the North. This formed an area in what is now Northern California, where the plates converged forming a Mélange. North of this was the Columbia Embayment, where the continental margin was east of the surrounding areas. Many of the major batholiths date from the late Cretaceous. As the Laramide Orogeny ended around 48 million years ago, the accretion of the Siletzia terrane began in the Pacific Northwest. This began the volcanic activity in the Cascadia subduction zone, forming the modern Cascade Range, and lasted into the Miocene. Events here may relate to the ignimbrite flare-up of the southern Basin and Range. As extension in the Basin and Range Province slowed by a change in North American Plate movement circa 7 to 8 Million years ago, rifting began on the Gulf of California.

The pacific and Nazca plates are forced under the north and South American plates respectively. Which create mountains on the western side of both American continents.