I'm trying to understand why if I consider a cylindrical capacitor whose height is $h$, the radii are $R_1$ (external) and $R_1$ (internal) and I put myself between the two plates I can say that the electric field is radial. My teacher says
For symmetry reasons
To my ears "symmetry reasons" isn't at all a reasonable explanation, I'd expect my teacher to explain what those symmetry reasons are but it didn't happen and now I'm struggling to figure out why. I already encountered this "for symmetry reasons" in another case, which is the spherical capacitor but in that case it was much easier to figure by myself: to achieve null electric field inside on the surface of the sphere the charge had to redistribute uniformly, and given any point of the space I could imagine my sphere as made of coaxial rings where of course the axis would be the radius from the center of the sphere to the point I was interested in. But now charge has to redistribute in a non uniform way to make the electric field null at any point inside, and I'm lost.