Just read this article by Jesse Enkamp. Not saying he is wrong (exactly) but there is more to it.

Read the article but as you read here are some points to consider:

1. There are two axes of rotation in the human body. Assuming proper posture, these extend horizontally through the points of the hips and vertically through the top of the head, down through the base of the skull and straight down to the floor through the tail bone. Where the two axes cross in the abdomen you find your center of balance, hara, "one-point", Svadisthana, take your pick.
    
2. The human body works best when the top of the head, shoulders and hips are parallel to the ground and the spine along with both legs is perpendicular to the ground. In general, this will place the points of the shoulders, points of the hips, center of the knees and center of the ankles directly on top of each other on both sides of the body (heiko dachi).
    
3. Front facing stances require the horizontal axis of rotation (through the hips) to be perpendicular to the target direction (zenkutsu dachi); while...
    
4. Side facing stances require the horizontal axis of rotation (through the hips) to be parallel to the target direction (shiko dachi; chiba dachi). These stances are solid and inflexible; power stances.
    
5. Offset stances require the horizontal axis of rotation (through the hips) to be at an angle to the target direction (kokutsu dachi, neko ashi dachi); these stances are fluid, flexible but weak; movement stances.
    
6. The universe works in circles and spheres and multiples of three more often than two. The circle is the strongest structure in nature. When the circle is divided by multiples of 3 it is strongest; when divided by multiples of 2 it is weakest. 120 degrees is the strongest angle you can hold; 180 degrees is the weakest.

Simple test: stick your arm out at 120 degrees (shoulder through the upper arm to elbow; elbow through center of the wrist) and have someone try to push your arm aside. Resist as much or as little as is needed to hold your position. Then, straighten your arm completely so it is horizontal to the floor and repeat the test. Do this again with your arm bent at 60 degrees and 90 degrees (shoulder through the upper arm to elbow; elbow through center of the wrist). See which is strongest.

So what does this have to do with kokutsu dachi/neko ashi dachi, you ask?

Simple: these stances will be at their strongest (and so will you) when the horizontal axis of rotation is level to the ground and at a 120 degree angle to the target direction. If you look at the images of "perfect" alignment in Mr. Enkamp's article you can clearly see this relationship.

BUT, you can take it one step further... if you examine the bend in the legs (both legs, all three of Mr. Enkamp's pictures) you can see they are also being held at a 120 degree angle. When you lift the front foot to rest on the balls of the foot, it changes the angle of the leading leg so you withdraw it slightly to restore both the 120 degree angle of the legs and the level aspect of the hips.  (Even further) If you look at the last 2 of his photos you will see the angle between the raised foot and the calf is also 120 degrees...

If you maintain the 120 degree angles and the level aspect of hips and shoulders you will develop a cat-footed stance that is at once both stable and agile.

But, what do I know?