They can, but it is not so simple. Some animals, even some fish, such as mudskippers and climbing perch, can breathe air pretty well, but have to return to water to moisten their various organs from time to time. Some such animals actually drown if kept under water too long.Some can be carried from dam to dam in moist straw and survive the journey.

Most fish have gills that are soft and collapse if they are taken out of the water. Being wet, those gills collapse into a into which mass the the air cannot diffuse rapidly. So such fish smother in air. The gills' skin cannot survive drying out, so one cannot simply dry out the gills to permit those fish to breathe.

As a follow-up on Jon’s answer. We also have to keep our cells in our lungs moist or else they will die. So, in the end we used oxygen dissolved in water, just as the fish do. The difference is that the layer of moisture is very thin and allows rapid movement of gas from the air to the cells of the lungs while the fish have to make do with water is dissolve in the mass of surrounding water.