Why do many fighter jets have double vertical stabilizers?
There are a few reasons many fighter/bomber designs have 2 vertical stabilizers:


one large tail produced more shear force at the root, 2 smaller tails mean less force at the vertical stabilizer root. This allows for a lighter structure
redundancy if one tail is damaged. The US navy philosophy is 2 is better than one, this makes sense given that its aircraft spend much of the time over oceans where there's few alternative landing sites
twin tails are shorter than one big tail, and vertical height is a consideration on carrier aircraft
twin engines spaced apart make for a wide fuselage back which can create a blanking effect with a single tail in the middle, 2 tails mean that there's always one vertical stabilizer that is effective
Twin tails create less of a radar cross section, and allow the tails to be angled to deflect radar signals away from airborne radar sources