One reason for having twin vertical tails on a supersonic fighter (not yet mentioned I believe) relates to the way the shocks behave and the interference effects between the fins.
Basically, at subsonic Mach numbers the two fins interfere with each other, in the manner of a biplane's two wings, which reduces their effectiveness as lifting surfaces (and thus their directional effectiveness). At a suitably supersonic speed, however, the two fins essentially move out of each others' direct interference, and begin to work like two truly independent surfaces.
It so happens that this kind of effect - where the directional stabilising effect gets more pronounced at higher/supersonic speeds - is just what the doctor ordered to overcome the increasing directional instability one finds due to the increasing effectiveness of the forward fuselage.
The alternative is to design a truly massive single fin sized for the high Mach number case and then cope with the excessive directional stability at low Mach numbers by other means.