This crossed my mind when I was reading this stata forum post, at which it is written:
SEM does not allow any endogenous variable to directly covary with any other variable, only regression paths and covariances between their associated error variables are allowed.
I get that the reason must have something to do with the fact that the exogenous variables don't have their causes specified, whereas endogenous variables do. However, I am struggling to express the reasoning in an intuitive way.
Why isn't it allowed? Why are regression paths and covariances between the associated error variables OK?