I think part of the reason is that the pressure is balanced. That is, the inside of our body is pressurized as well as the environment outside our body. When the balance is disrupted, you can feel the pressure. For instance if you have a mild cold and your eustacion tubes to your ears are swelled shut, and you are a passenger in an airliner that is descending, you feel the increasing atmospheric pressure during the descent ( sometimes painfully so) because the inner part of the eustacion tube can’t equalize the pressure