We aren’t really as soft of cushions as we think we are, but how does catching someone reduce the chance of them getting hurt drastically or they were to fall from the same height?
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Two reasons.
First, while we’re not as soft as cushions, we are considerably softer than, say, concrete. That difference can make a big difference! (The downside for the catcher is that they’re also more fragile than concrete.)
Second, think of catching a ball – usually you’re not holding your hands out rigidly. You’re pulling your hands back to slow the ball down more gently (this both helps stop the ball bouncing out of your hands and means it’s less likely to hurt you). If you’ve ever thrown a baby up in the air and caught it you’ll (hopefully) have done the same. So they’re not just hitting into you and squishing you, you are starting off with arms extended and using your strength to decelerate them more gently.
Of course, this does depend on the speed, size and weight of whatever you’re catching. It’s one thing to carefully catch a baby, another to do the same with a full-grown person.
G force is what kills. When you fall and land on a hard surface, you descelerate very very quickly. From what ever speed you were going to stop. At a small distance that might be just a few Gs of force. As you get higher, that number gets higher. Eventually, the g force you would experience would be too high for you to survive. Hundreds of Gs, even thousands.
To prevent this, you just need to spread that force out over a longer period of time. the longer time you take to slow down, the less force you feel.
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