It happens so quickly most of us don't get to consciously choose how to react.
Even with highly trained pros in their prime, look how they fall. Most of the time they have little or no time or control over how it happens. There are a few exceptions, cyclists with superb reflexes. Most just fall the way any of us would.
I've watched several casual, recreational riders fall and have never seen anyone show any ability to control their fall, roll with the fall, etc. Even at slow speed we go from vertical to horizontal in a blink. It's not like Grand Prix motorcycle crashes when the rider is leaned into a turn and feels the bike slipping away, so they slide with it.
Last week I slipped on an icy puddle. The temperature was in the 50s so I'm guessing it was left over from sleet or hail the night before.
Fortunately I was traveling less than 10 mph. It still happened so quickly I have no idea how I fell. I can only guess from looking at the wet and muddy streaks on my kit that I was holding the handlebar and fell on my right shoulder and hip, rolling back slightly. I certainly didn't consciously roll with the fall. Maybe instinctively, but it's been decades since I practiced martial arts and I learned long ago those tricks are all "use it or lose it." If you don't practice falling regularly, you probably won't do it properly in an emergency.
Surprisingly I didn't re-injure the shoulder that was broken and dislocated a couple of years ago when I was hit by a car. The surgeon who examined my injury and X-rays a couple of years ago said I probably landed on my shoulder and didn't try to reach out with my arm/hand to break my fall -- no evidence of injury or bruising to the elbow or forearm, which has happened on previous minor falls with only scrapes and bruises. I don't remember. That incident also happened too quickly.
But since then I've done a lot of physical therapy to strengthen the upper body. I have early onset bone density loss that isn't responding to supplements (due to a thyroid problem, not the alleged bone density loss with pro cyclists), so I need a little more cushion from muscles.