The skinny jean showcases the discrepancy between the size of your thighs, and the size of your ankles. Since your thighs are much larger than your ankles, this causes your thighs to appear very large, simply by comparison to the size of your ankles. In flared jeans, the size of your thighs is offset by the flare at the ankle. This causes your lower and mid-thigh area to appear more lean, because the lower leg appears to be larger. Its a wonderful illusion.
Lets take a look at a more common scenario; a woman who doesn't have skinny little legs.
In the picture of the skinny jeans, notice that the mid-thigh appears to be the largest area of the leg, and the knee lacks contour, causing the leg to have a sausage-y look. In the flared jean, the lower thigh and knee area appear to be quite slender, thanks to the complementary flare in the lower area of the pant.
To further demonstrate my point, take into consideration the way that an hourglass figure may be flattering to the waist.
Large breasts and wide hips cause the waist to appear small, by comparison. While on the other hand, small breasts and narrow hips can cause the waist to appear larger than it may actually be. Another wonderful illusion for those women blessed with breasts and hips.
Hourglass waist, hourglass pants... Same concept, equally effective.