About drinking from faucets
From 101 Questions Your Cat Would Ask Its Vet If Your Cat Could Talk by Bruce Fogle
Why do I prefer drinking water from a dripping tap rather than from the water bowl that people kindly fill for me?
Simply because it is fun. Some people like to do the same, only they use the garden hose....
Cats drink by cupping their tongues into a classical spoon shape and lapping. Taps drip perfect proportions of water to fill the cup.... Finding his own source of water satisfies a cat's need for mental stimulation. Rather than drinking from a boring bowl marked 'CAT', he leaps up, treads warily amond soap and utensils, then leans forward and drinks from his own natural waterfall.
Finally, unlike many other species of mammals, cats can taste water. They have special taste buds for doing so. It could simply be that fresh running tap water tastes better than water that has been sitting in a bowl for several hours.