The key to the origin of the word “catwalk” is that it refers to a narrow footway or platform. We know that cats are very surefooted and frequently negotiate the tops of fences and other narrow walkways such as branches with ease. Their athletic ability in this regard is one of their defining features. A natural consequence of this is to describe a narrow walkway or platform as one that is suited to a cat and therefore why not call the platform a “catwalk”?

Dr Desmond Morris in his book Cat World tells us that the word was originally used to describe a narrow footway along a bridge and then later became a common term for a high walkway above a theater stage, inside an aeroplane or in various military contexts.
Nowadays it is used to describe a narrow display area on which fashion models parade at high profile fashion shows. Morris refers to a book written by Jean Conger called The Velvet Paw in which the author writes “this name began at the bridge, and with the idea that puss would be very careful to make any bit of dry land hold his footsteps, because his dislike of the water”.
The Online Etymology Dictionary says that the origin of the word “catwalk” dates back to 1885; meaning a “long, narrow footway”; a narrow passage that needs to be crossed carefully. The key word here is “carefully”. This is a reference to my original statement in the first paragraph namely that cats are surefooted and are therefore instinctively and naturally careful when navigating a narrow pathway or platform. Such a platform is made for a cat hence it is named after the cat.