> if I was walking toward the black hole past the event horizon, and then I turned around

Note that, once you're inside the horizon, you can't "turn around" and go back outside again. You're inside the hole for good.

And once you're inside the hole, yes, no matter which direction in space you move, you're moving "towards" the singularity. But a better way to look at it is that the singularity is a moment of time, not a place in space. You're moving "towards" the singularity in the same sense as you're moving "towards" next Tuesday. You can't stop moving towards next Tuesday by changing which direction in space you move. The same is true for the singularity once you're inside the hole's horizon.