Clients and business people are typically too close to the problem to be able to really see what it is. That is why a business analyst can be so valuable. A BA can ask the right questions, step back from the symptoms, and see the real problem. Many times the client really doesn't know what the problem is, just that there is a problem. Our job as business analysts is to help the clients identity the real problem and make sure the problem is worth solving (aligned with organization strategies and goals, high priority in the scheme of things, cost beneficial to solve, etc.).
The requirements are what is necessary for the business to do both from a business perspective and technologically. Consider this: if the client knew what the problem was and the requirements - what to do to solve it - what would the client need you for?