Why can fish breathe under water but land mammals can't? How can fish extract oxygen straight from water but humans can't?
I'm taking this question at face value. Yes, fish have gills, but we also have a respiratory surface in our lungs so why couldn't we 'breathe' water and extract the oxygen (since extraction is a simple matter of diffusion from the content of the lungs into the blood).
Apparently we use 550 L of pure O2 per day. This works out as approximately 400 g.
The solubility of O2 in fresh water is around 10 mg L-1. Assuming a hypothetical situation where we could breathe water and extract all of the O2 from each lungful this means that we would need to breathe 28 L of water per minute, compared to the 8 L of air that we breathe.
Now of course water has a much higher density than air so that a lot of energy would be expended in moving this much water in and out of the lungs (which in turn would require us to consume more oxygen). Couple this with the fact that realistically we would only be able to use a fraction of the O2 dissolved in each lungful and you can begin to see why this is a non-starter.
Gills allow this problem to be largely circumvented by having a one way flow of water over the respiratory surface, which in the case of fish is often achieved at least in part by moving through the water.