So you need to consider the system in which this process is occurring and how physical properties of gasses depend on such systems. Let me elaborate...
Your respiratory pathway is an open system exposed to the ambient natural pressure. In order for your system to deviate from the normal negative/positive pressure respiratory cycle, you would have to close the system. Herein lies the crux of the problem, any gas system that is open and exposed to the external environment will have a gas pressure equal to the external environment...because there is no boundary, and remember pressure is [Force/Area]. So when the air in your lungs saturates with water vapor, it "kindly" pushes other gas molecules out of the way, and since there are no boundaries such as a sealed container (assuming you are breathing here), the gas molecules shift are free to move to the external environment.
Now think about this concept as a standalone:
Imagine you have a tank full of helium and you are standing in the middle of a football stadium. You have a pressure gauge that reads the ambient environmental pressure and watch it as you release the contents of the tank. Do you think that the gauge will read an increase in pressure or do you think that the gas you just released will just vent into the atmosphere without ever registering on the gauge? No imagine if you were in an air tight room and did the same thing...the gauge you are reading is the pressure in the room. You vent the tank, but since the helium can't escape the room, you just added a bunch of new molecules that will bounce around the "container". Now since we know that the pressure exerted by a gas is the physical result of the gas molecules bouncing off of a surface, in this case a wall, we expect that more collisions at a given T would mean an increase in pressure.
more molecules-->more collisions-->more Force/Area=increase in pressure.
On a side note: any fluid or gas that is freely exposed to the atmosphere without boundary walls (pipe, piston/cylinder, etc) will instantly assume the pressure of the ambient. The result of seeing water flow out of the hose after it has left the end of the nozzle is due to its inertia and momentum, not because it retains the pressure it had within the hose itself.
