Depends on your definition of Universe. If you think of the Universe as everything we can see, then that universe started with the Big Bang. If you think of the universe as more than just that which started with the Big Bang, that is beyond or before the Big Bang so to speak, then I agree with you that the Big Bang didn't start that universe. However, the point is that scientists seem to claim that the Big Bang started with an infinitesimally small point of energy. Now, did that point have no size or some very very tiny size? It would seem to me that even the point that started the Big Bang must have had some size, because it existed. This is similar to the argument that zero must have some size (however tiny) just to be able to claim it exists.