Legal Question in Construction Law in California

Architects are not required to carry E&O insurance in California and most residential architects I know don't carry it. However, if you signed a contract with her (or your emails are deemed to be the equivalent of one, depending on their content) and providing you insurance was a prerequisite to you paying for her services, then her refusing to provide it to you would potentially be grounds for canceling the contract. On the other hand, if you had her do the work, she did the work, you accepted it and now just don't want to pay her, chances are you will be deemed to have waived that requirement of the contract and would be obligated to pay. Your question doesn't really provide enough information to fully answer it.