I am having trouble understanding Gauss's Law. Suppose we wish to find the electric field strength between two parallel plates with charge density $\sigma$. I know it should be $E=\sigma/(2\epsilon_0)$.
But if we place a cylinder between the plates with base parallel to the plates such that the cylinder does not intersect the plates, then the charge enclosed is $0$ and the flux is $2EA$ where $A$ is the area of the base of the cylinder. Thus by Gauss's Law, $2EA=0$, which gives $E=0$. What is the error in my understanding?