I've got the same problems, slipping off the rock is to easy. Once we're in the air we should be able to open the parachute ourselves.
Yesterday I dropped from a huge stone bridge, had about 5-10 seconds to open my parachute. Nothing happened.
Then I stood on a much smaller cliff, pressed x and he made a ~20m basejump.
Same here. I thought that this mechanic would be more like Far Cry, where you can open your parachute off of pretty much any ledge that's taller than the player, but I haven't managed to open it once. I just seem to slide down the side of whatever cliff my character is on in lots of short hops and it won't activate.