You can dissipate a lot more energy than you can produce with your muscles. For example, you can comfortably drop much more than you can jump.

Your comparison of throwing and catching makes me think of the Caber Toss. Where a 79kg wood trunk gets, well, tossed.

https://en.wikipedia.org/wiki/Caber_toss

The key to this, and to mentioned in the article, is accelerating/decelerating not the object, but the centre of gravity.

Or carrying them up a flight of stairs on your back. I think peak power is more important than work here. The peak power to throw someone 3 metres into the air is ludicrous, but arresting a fall over a (slightly) longer time period, with bones and ligaments taking the peak power instead of muscles are what is going on.

> with bones and ligaments taking the peak power instead of muscles

That's kind of an odd way of phrasing it; I would have said something along the lines of them providing the upwards force through tension rather than bringing power into the discussion.

It's the time derivative of work, seemed natural to me. Also muscles use rate limited chemical reactions to move, so it is a reasonable assumption to model them as power limited (with different regimes for different metabolic mechanisms). So when talking about the limits of what a person can do with their muscles, power limits seem important.

Likewise impressed, but the fireman's own body transmitted much of the force to the window frame. So it's less the equivalent of launching someone into the air, and more like hanging on to someone while you are launched into the air by harness.