Why don't the customers know their own problem?

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?

When agile arrives move up

So management has decided to change software development processes to a more agile approach. And that means you, the business analyst, need to adopt a product owner role, or perhaps a scrum master if that's the way they go. In any case, your old rituals of gathering information, analyzing it, and producing an extensive set of requirements amidst negotiation, mediation and lots and lots of meetings are no longer going to be needed. So what do you do? Step up.
Someone has to evaluate whether the problems the product owner wants to solve are aligned with organizational strategies and goals. Someone has to verify that the solution that comes out of the iterations will not adversely impact other departments or processes. And someone has to coordinate, on the business side, with the other projects that are in process at the same time.
And that someone is the business analyst. Who better?