Humans and whales are warm blooded animals. Whale breath like mammals because whale can't extract so much oxygen dissolved in the water. When inside the water whales does not breath instead they have developed a machaniam to hold the breath under water and come on surface to exhale and take a New breath. oxygen requirement for fishes is very low because fishes are cold blooded animal and fishes have gills which allow fish to expel the water out and take the dissolved oxygen in for respiration.
Human are warm blooded animal and their oxygen consumption rate is much higher than cold blooded animals. Humans do not have gills so they can't extract dissolved oxygen from water. The lungs of human does not have large surface area so that they can absorb the large amount of oxygen and can use it gradually when not taking air in. Another reason is concentration of oxygen is very less in water as compare to oxygen concentration in the air, as we know that we are able to inhale oxygen because of partial pressure of oxygen is many times greater than partial pressure of oxygen in the blood, making a pressure difference which allow oxygen to move from atmosphere to lungs. But in water due very low dissolved oxygen concentration the partial pressure difference of oxygen is not enough to make oxygen move from water to lungs. In air oxygen concentration is 9 mmol per litre while in water it is 0.44 mmol per litre. So there is 20 times as much oxygen in air as dissolved in water. If we try to breath under water we will end up with accumulating water in the lungs qhich cant be expelled out through exhalation like air and will lead pulmonary edema which could be fatal. So human respiratory system has developed in such a wsy that make us completely unsuitable for aquatic life and if we try to stay for longer period of time under water it could be extremely fatal for us.
Underwater, we humans can't compete with whales and other air-breathing marine mammals, which can stay submerged...