Falling forward means you are sliding forward out of the saddle, and/or you can't easily support the weight of your torso using the strength of your back and legs.

So if you keep sliding forward in your saddle, your hands have to push back.
The stronger you are, the more you need to lean forward to counter the driving force of your legs. So as you gain fitness, you tend to support less weight with your hands, and need to lower your position so you don't wind up pulling on the handlebars constantly.

This is why people think you need to lean forward to be efficient and aero, but that isn't true until you have the strength to match. This also applies to the intensity of effort you will be making. Even a fit person will sit more upright on a bike that is for slow cruising, and lean forward on a touring bike where they will be going slow in spite of big efforts.