Solar eclipses don't make complete sense

The total width of a solar eclipse is roughly 100-160 miles wide. However, if the moon where to completely get in front of the sun, then how is there only 100 mile wide shadow when in fact they claim that the moon's diameter is 2159 miles wide. If you have a light source like a flashlight, then put your hand in front of it - does the shadow on the wall get larger or smaller? It clearly gets larger. Therefore, my assumption is that the solar eclipse should actually cast a larger shadow than the size of the moon. It should be possibly 3000 miles wide, not a tiny 100 miles wide.