Why is inductance negative in this triphase mutual inductor?
A negative inductance would imply that the current is dependent on voltage varying with time but also negated. (i = -Ldv/dt instead of i = Ldv/dt ). No one can build a physical inductor that will automatically flip the voltage coming into it, but it makes for an easy analysis. A circuit representation is a way to model the physical world. 

With models you can get results that are not physical, that model the system of interest just fine. An important part of electrical engineering is being able to model systems, but also realize the differences between the model and the real world. There are also no ideal circuit elements, there are no capacitors, inductors or resistors that have don't have parasitics. 

For most things the parasitics don't matter (do you really care if your resistor has a few nanoHenries of inductance when your creating a voltage divider? No, but you will if your trying to run a GHz signal through it).