Does it have to do with the interdependence of one equation on the lagged values of its own as well as the other equations?
If I remember correctly, in simultaneous equations, cross-causality is also a cause for endogeneity, but in VAR models, the causality moves in one direction, the past impacts the future and not vice-versa.
So why are the variables in a VAR model considered endogenous? Does it have to do with the interdependence of one equation on the lagged values of its own as well as the other equations?