In special relativity, we know that if an inertial observer $A$, having a relative motion WRT an inertial observer $B$, attributes, say, time dilation and length contraction to respectively $B$'s clocks and rulers, $B$ can do the same to $A$'s too.
However, I want to know why this is not the case in general relativity. Assume $A$ is located on a massive planet, and $B$ is a Schwarzschild observer both at rest WRT the planet. If $B$ measures $A$'s clocks run slower and his ruler contracted, $A$ detects vice versa, i.e., $B$'s clocks run faster and his ruler is possibly expanded. Why is this the case? What happens to symmetry? Is it because, in the latter example, one observer ($A$) is non-inertial and the other one ($B$) is inertial?
Moreover, please explain which ruler (radial or tangential) is contracted or expanded, and in which directions the speed of light is measured smaller or greater than $c$ from the viewpoint of both $A$ and $B$.
As far as I remember, radial rulers are left unchanged from the viewpoint of both of these observers. Is it correct?