Why shouldn't extension leads be coiled up tightly when in use?

This is because it is acting like a transformer. A transformer is made by tightly coiling insulated wire neatly in parallel around a rod or tubing, and it generates a lot of heat. One of the worst things you can do is to use an extension cord while it is still neatly rolled up around a core of a drum. It is then behaving like a transformer and the lead cord gets quite warm. The reason extension cords should not be used while coiled is that the heat melts the plastic insulation around the cord, the now-bare wires short-circuit, and it will explode . Uncoil extension cords before you use them.