Compatible with the laws of physics

There are many things that might at a glance feel like they violate some physical law:

• A person can cool themselves with a fan. But how is that even possible: a system lowering its own temperature?
• In space travel, a craft can pick up speed by suitably grazing celestial bodies. Isn’t that generating energy for free from somewhere?
• With pulleys you can lift things heavier than yourself.
• One can sail faster than the wind.

This classic problem also comes to mind:

You have a liter of red, 100-degree water and a liter of blue, 0-degree water. You can divide the water into cups and, by waiting, equalize their temperatures in proportion to their masses (e.g. pour 1 dl of red water and 4 dl of blue water into cups and wait, whereupon the water in both cups settles to 20 degrees). Assume there are no heat losses. Is it possible to get the average temperature of all the blue water above 50 degrees?

I’ve indeed heard someone answer quickly and confidently with “it’s not possible”, because at first it sounds like it would violate some conservation law. (Spoiler: it is possible.)

I wonder if people’s intuitions have been distorted by all the warnings about various wacky ideas violating the laws of physics, building a perpetual-motion machine is impossible and so on, so that we then over-generalise that even to things that are possible.