Though most volcanoes are mountains, most mountains are not volcanoes, why or why not?

Look around you. If you live in a part of the world where there are mountains but no volcanoes, you must be far from any subduction zones, spreading centers, or "hot spots." For example, if you live in the central or eastern United States, chances are you have never seen a volcano. If, on the other hand, you live in the Pacific Northwest, Alaska, or Hawaii, you are actually living close to (or even on top of!) a volcano. That is because the West Coast of North America is part of the Pacific Rim of Fire. If you live in the Mountain States, you are near one of the best known "hot spots" in the world: Yellowstone National Park. Though there are no volcanic mountains in Yellowstone, there is lots of volcanic activity, resulting in such dramatic features as Old Faithful geyser. In fact, Yellowstone lies at the active surface of a molten cauldron deep within the earth that once fed an immense volcano, now collapsed and referred to as a caldera.

Many volcanoes remain dormant for a long time, because they started erupting a long time ago, while mountains usually are made by tectonic plates shifting up and down, like mt Everest, but they usually don't contain magma. I seriously hope this is what you are looking for, because this is my best answer XD.