Lighting Should be Deliberate
Lighting the face/person properly is more than just putting a light to one side of the subject and firing away. Placement, intensity, and most importantly doing so in a way that creates the look you want is essential. And lighting plays a huge role in the look for a headshot or portrait. Take the 2 examples of the same person below. For the image on the left, the shadows are fairly narrow (known as "hard light") and the camera left side of his face, particularly the ear on that side, is pretty "hot" or the brightest area - and the white shirt is catching a lot of the light (the shirt is pointed directly at the light), which distracts the viewers eye. Contrast that with the image on the right - the highlight or brightest part of the light is in the middle of his face, and the light falls off as you move towards the ears. Our eyes are drawn to his eyes/mouth, which is where expression comes from and where we want the viewer to look. This is not to say that you always want the face to be shadowless - when done properly, shadows can create drama, mystery, power. But those shadows need to be controlled with careful placement of the lights.