There is difference between a steady current and current when switched ON and OFF. Steady current is less than the switch ON current.
Any equipment with inductor load like motor, fan etc draws higher current at start. Even a light bulb, even though it is a resistor, due to its cold start, draws little higher current when switched on.
When a load is switched ON again and again, the increase in current heats the fuse wire moe and more. This heat makes the fusing.