because the light source (from the viewpoint of the subject) gets smaller
That's a good answer in practical terms. Dave says that it gets smaller from the viewpoint of the subject - think of it in terms of getting smaller in relative terms, i.e. that it gets smaller relative to the subject. It might help, because light gets harder when it gets smaller in relative terms.
Think it terms a large light source such as a softbox that is twice as wide as the subject.
Now, that large light source will light the subject from various different angles, it will light it from the middle, going straight to the subject, it will light it from each end, lighting the sides of the subject to some extent (often referred to as wrap around lighting) and it will light it from every intermediate point too. Each tiny point from that softbox (lighting source) will be its own lighting source and will create its own light. therefore each tiny point will create its own shadow, and those shadows cross over each other and soften all the other shadows created by the other point sources of light. As you move the light further an further away, the point sources of light get closer and closer together in practical terms and eventually, if you move the light far enough away, all of those millions of point sources become almost a single point source, creating a single shadow instead of a complex set of shadows.
Example: The sun. It's massively bigger than the earth but because it's also 93,000,000 miles away it looks small. On a clear day with no clouds it becomes a small light source in practical terms and so casts a single hard shadow. On a cloudy day, when you can't see the sun, the whole sky becomes the light source and is similar to a very big softbox, the light is coming from so many different directions that all the shadows overlap and merge and you can't see any shadows.
There's a lot more to it than that, but hopefully it helps, without getting complicated.