Software quality is rarely a selling point, it's only that the noticeable lack of quality in your product can be a selling point for your competitors. No matter what you do, you'll never have enough staff to do what you'd like to do. The requirements and specifications for the product, most of which will never be written down, will be vague, or outdated whenever you do see them. But each functional team also needs a more specific mission that contributes to the whole. In well-run projects, the mission of the test team is not merely to perform testing, but to help minimize the risk of product failure.
Testers look for manifest problems in the product, potential problems, and the absence of problems.
They explore, assess, track, and report product quality, so that others in the project can make informed decisions about product development. We are not out to embarrass or complain, just to inform. We are human meters of product quality. The heart of testing is examining a product system, evaluating it against a value system, and discovering if the product satisfies those values. To do this completely is impossible.