The evaporation of water drains heat from the body of the animal (this is a common cause of hypothermia), requiring the animal to burn calories to maintain its body heat, calories better spent hunting, mating, keeping your immune system ( or caring for other members of the community (family, flock, herd...).
Also, the evaporating water might make small particles from the animal's fur, feathers or skin airborne, thus spreading the scent of the animal over a larger area than usual, attracting predators.
Yet another reason is the disabling effect the water might have on the fur or feathers of the animal. In cold weather, an ice crust might form on the wet fur and the moist might accumulate snow and grime, and the extra weight of the water might make flight impossible.

Trust me on this; I've got fur.

Or more specifically cats. Actually, that is a fallacy, and many cats like water. Indeed, bobcats like water and fish in streams. Cats' fear of water is actually evolutionary, beacuse when kittens get wet (e.g. in the rain) they have to be dried off very quickly or they get hypothermia and die. This is because, I think, they have thick fur and absorb lots of water, but cannot support the loss of heat by evaporation because they are only very small. This fear carries through, in some cases, to adult lives as well.

As well as this, having today spent a lovely day out at Southport Pleasure Beach in typical British weather, I can also see why humans do not enjoy the rain: Firstly it ruins clothes and makes them soggy, sticky, and uncomfortable. This lasts for hours if you do not have a change of clothes handy. Secondly, it makes you cold, wet, and miserable, especially when you are with children.

Of course, this only applies in the cold. Most humans enjoy getting soaking wet when it is hot, as the evaporation then allows the body to cool down if perspiration is not working quickly enough.

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