In a domestic circuit, switches and fuses are connected in the live wire. This is because the live wire is at about 230 V, while the neutral wire is at about 0 V.
When a switch in the live wire is open, the appliance is disconnected from the 230 V supply. All of the appliance is then at about 0 V compared with earth, so it is safe to touch.
If the switch were in the neutral wire, the appliance would still be connected to the live wire when the switch was off. Parts of it would stay at about 230 V, and a person touching them could get an electric shock.
The same is true for a fuse. A fuse in the live wire cuts the appliance off from the live supply when it melts. A fuse in the neutral wire would melt but leave the appliance connected to the live wire.