How not to squeeze out customer mind by eliciting the project goal

You do not have to answer to your customer. Projects are created to create a product/service/result that will allow the organization to achieve their strategic goals solving the business problem. Project manager is not in charge to define the product/service/result.. From product/service/result definition the project manager will create all related to project including the project goal. Your focus are project requirements that must be defined from product/service/result requirements. Project goal is the meassure of project success or failure then you have to stablish your project goal based on: scope (you will create all that was defined in the product/service/result scope), time (you will complete the scope in the time needed as defined by the window of opportunity), cost (you will maintain project costs as defined like a component of the budged), quality (you will create what is defined and exactly as defined). That´s all you need.