Is it correct English usage to say climbing down the stairs?

Answer 1

No. You walk or run down the stairs. Climbing is only used, perhaps incorrectly, for upward travel on stairs. You can, however, climb down a rope, or a ladder.

This clearly shows how odd the English language can be.

We can climb up a ladder or climb down a ladder, but we only climb [up] the stairs. So, what gives? When we climb the stairs, the word up is implied.

The word climb has two main usages, an intransitive one and a transitive one. In its transitive sense, the direction is upward. We climb mountains. We climb stairs. Also, ivy climbs the walls. But its intransitive sense doesn't necessarily imply a direction, although in some usages, it can. (Confused? I know I am!)

One intransitive sense is synonymous with "rise." Stock prices will climb if interest rates are cut. Another sense is "to ascend using the hands and feet." I had to climb the ladder to reach the second-floor window. But a third sense requires the writer or speaker to provide a direction. After the paint splashed me in the eye, I climbed down the ladder very unsteadily.

Perhaps we don't hear "climb down the stairs" because we don't use our hands and feet to go up or down the steps, and the word climb conjures up the image of using both the hands and feet, as one would do if he were ascending a ladder, or a rope up a rock face or mountain.