Why is it not advisable to fuse the neutral
Cost: One fuse in the live is adequate to cut current to the circuit.
Isolation: If the neutral fuse blows first the circuit would stay live. It's generally best to disconnect the circuit from mains.
Polarity: Many countries don't use polarised plug and sockets on single-phase plugs. This means that the fuse in the appliance may indeed be in the neutral. So, to answer your question, "Why is it not advisable to fuse the neutral?" - we do it all the time in many countries.


 

Figure 1. Unpolarised American (120 V) and European (230 V) mains plugs.

Update:

Note that with the unpolarised plugs the fuse can only be guaranteed to protect against over-current in the device itself. e.g., a motor short-circuit will cause the fuse to blow. With the fuse in the neutral wire a short to earth would not cause high current to flow through the fuse.