I was listening to some RealATC this evening and came to this one about an accident at LaGuardia airport. This question is not about the accident in any way, but I am using this video because it has an example of what I mean and has a labelled diagram as well.
As the clip advances, it becomes clear that at that time, planes were landing via ILS Runway 13. However, planes were being directed to takeoff from Runway 4.
Under what circumstances might a major commercial airport have planes landing and departing via crossing runways, instead of on the same, or at least parallel?