Intentional Injury and Coverage under the CGL Form

Our insured has a standard CGL form. The insured was recently sued and the allegations in the complaint stated that our insured intentionally caused injury to the plaintiff. The insurer is denying all liability including defense because the allegations use the word “intentionally”. We disagree with this stance.

We believe that general liability coverage defends and indemnifies the insured for all allegations for bodily injury and property damage brought against an insured in civil court. There was no criminal activity involved here, so is the insurer correct in denying any coverage?