Understanding the symmetry argument in determining induced electric fields

I am trying to understand how to determine the shape and direction of the electric fields induced by a changing magnetic field. But all of the resources I have read make use of the following symmetry argument which I don't understand:

Consider a magnetic field increasing in magnitude at a constant rate. The magnetic field can be generated by an ideal solenoid. Then, by way of the symmetry argument, the electric field induced by this magnetic field will be circular in nature.

I'm not sure what is meant by symmetry here. Does it mean:

The electric field set up will have to be circular because the magnetic field within it uniform in magnitude and distribution (at a differential time dt), thus to oppose this flux, there has to be a symmetrical magnetic field created by the induced electric field.

For any given coordinate $$\theta$$ the distribution "looks" the same.
This means that the field value for all $$\theta$$ will look the same (provided the homogenous solution is zero).