A liability insurer has a duty to defend its insured against third party claims that are potentially within the scope of the insured’s policy, and also has a duty to defend any noncovered claims that are asserted in the same action.
An insurance company may be excused from a duty to defend only when the lawsuit filed against you raise no conceivable theory which could bring coverage into play. In determining whether a claim creates the potential for coverage under an insurance policy you have to look at the interpretation of an insurance policy. In determining policy interpretation you have to look at the the language of the contract in order to ascertain its plain meaning or the meaning a layperson would ordinarily attach to it. You don’t have to accept the interpretation your insurance company determines to deny coverage.