My guess that your mesh is symmetric, but the symmetry axis is rotated. for example you rotated your Mesh in object mode. I am pretty sure that you did something like that, because you presumably used the default 32 vertices number cylinder, and in that case 4 vertices must be aligned to the coordinate axis by default, if you add your object to the center of your world, without tweeking the Add circe tool option... so it should look like this:
Delete your extrude.
Rotate your object (in object mode), to make the axis "cut half" the edges. Like this:
Apply rotation (Ctrl-a)
Recreate mirror modifier, and you good to go.
In the future for similar objects, you should rotate circles/cylibders like this if you wan them have symmetric handlers.The general formula for rotation for blender circle:
360/vertices_number/2 (if you use degrees. You can write it directly to the rotate property field)
(it will not work on your current object, because it is already rotated)