If th4 cab owner/driver is insisting on FIR against you, it is better you also lodge a complaint on the cab owner/driver narrating the incidence. It is always safer to lodge a complaint from your side too or else you will be liable for the insurance claims.
You cannot expect support form police in this regard who will act on the basis of graft received by them or on the basis of the pressure from any higher authority.
Your counter case would make him to a negotiable platform where you can dictate terms and make a counterclaim against him for the damages you suffered.