One of the most important things about working with any organization is learning how to work with other people -- on a team. It is learning how to listen, to advise, to influence, to accept, to motivate, and follow.
The best programmer may not be the best person for a job -- or for a start-up because while they know code, they may not know people. the most creative designer must know how to sell their design to people. The best engineer maybe the one that can facilitate a team of people to solve a problem.
I would expect that a start-up would find the intern that has learned all they can learn after a couple weeks from a specific assignment to be rather impetuous. As Alain says -- impatient. I would find it to be a reflection of an individual who had much to learn about how people work together. What a great opportunity for you in your desired and eventual role in your own start-up.
What to do?
In any good internship situation , you should have scheduled regular meetings with your direct supervisor to review your learning goals and progress. If you do not have such a meeting scheduled-- get one on the calendar now. Articulate your expectation that you will have an opportunity to review your performance, and more specifically your progress toward reaching your goals for the internship. If you have not laid out goals for the internship-- then make an agreement upon those the desired result of your first meeting. Within the context of reviewing with your supervisor the progress on the learning goals -- if you can present that you have learned what you can from your current assignment and engage your supervisor in exploring other potential projects to work on (like the one you have your eye on) then you will be very successful in both learning about that project-- and how working in an organization . . .well, works.