Question

why the two poles of magnet are considered inseparable

Answer 1

The superficial answer is that the poles do separate, but at the instant the magnet is broken two new poles form so that both pieces have two opposite poles. Two new poles form because at all scales down to that of individual atoms the pieces act as if they have two poles. This isn’t noticed internally because where neighboring pieces are adjacent along the line of the magnetic field their opposite poles are nearly in contact, and some of the effects cancel. Really the magnetic field is almost entirely confined within the magnet itself..........hope it will help you dear