Why should I never look directly at the Sun?

You must not look directly at the Sun during an eclipse for the same reason that you must not look at it under normal conditions. But the eclipse can trick you into thinking it is safe.
During an eclipse, the ambient light dims and your pupils dilate. Although it may seem safe to look, such wide-open pupils allow more radiation to enter all at once, and the damage can be even greater.
The Sun continues to emit dangerous radiation even when it is partially covered by the Moon. It emits very intense ultraviolet and infrared radiation. Ultraviolet light burns the cells of the retina, and infrared radiation heats and damages the tissues of the eye, even though you may not notice it because the retina has no pain receptors. The result can be solar retinopathy, an irreversible injury that causes blind spots or permanent loss of vision.