I think a possible analogy would be to imagine that the singularity is a waterfall. By emitting light, you are trying to send a signal upstream using a tame fish. Outside the event horizon the fish is able to make headway against the current. But the river flows so fast within the event horizon as it approaches the waterfall, that your fish ends up going over the waterfall shortly after you do because the river is flowing faster than the fish can swim.
Note that at no point does the fish change direction and it moves with respect to you at "the speed of fish".

This "river model" for a black hole is discussed in detail by [Hamilton & Lisle (2006)][1].


  [1]: http://opscience.iop.org/article/10.1070/PU1976v019n07ABEH005277/pdf