Well, the first reason might be that I don't have jumper cables, which would make push starting the best option. Of course, push starting only works if you have a manual transmission car. If it's an automatic, push starting won't work so your only choice would be a jump. I'm not sure about the new CV transmissions, but I suspect they won't push start either.
If I had a manual transmission car and had a choice though, I would go with push starting every time. It's just less hassle. a quick push, pop the clutch and I'm on my way, already behind the wheel and in motion.
With jump starting, first you have to have another car, then you have to pop both hoods, hook up the cables, try to start the car, oops - bad connection, jiggle the cables, start the car, unhook the cables and stow them, drop the hoods and then drive away. I once jump started a guy and after we did all that, the first thing he did was stall it when he went to drive away. We ended up push starting it anyway.
I've never heard of cars that will start with only a jump or only a push, but with the newer, so called, "improved" technology, it wouldn't surprise me. I guess that's why I tend to stay with the older, simpler designs. There's just a lot less to go wrong. I like having a vehicle that I can start with a quick push.