system
Given the following post, respond as if you're commenting on Reddit:
human
Why do our hands get sweaty when anticipating strenuous activity, and are often the first things to sweat? What kind of survival situation is benefited by slippery but slightly cooler hands?

Is this just poor adaptation? In many sports - e.g. weightlifting, climbing - and work activities people need to chalk up their hands or wear tape or gloves for grip, purely to counter this crappy response from their body. I would imagine in a fight or flight situation, evolving humans needed grip much more than they needed a marginal amount of heat dissipation from their hands.
gpt
In evolution terms, sweating has been around a lot longer than hairless bodies. So although it is complex and there is no definitive answer, you can't rule out the possibility that hand sweat under stress was a way to cool off as much as possible  in anticipation of overheating from back when body sweat was not very useful due to body hair. We lost most of the hair, gained a lot of sweat glands all over the body, but still have the older stress response. 

And, as others have noted  moisture generally improves grip of organic material (trees, rocks,) even though it is a hindrance to modern polished materials (metal, plastic.)