I have been reading a few articles about the question why we don't feel/notice gravity in everyday life, but I couldn't understand why exactly we don't feel/notice it, that is, why we don't feel a strong force pulling on us at every moment.
Answer
Theoretically, the only unambiguous way to "feel" gravity would be to travel near an extremely strong source of gravity, or rather an extremely strong gradient of gravity (e.g. a black hole), and feel tidal forces from such a massive object. (that, or gravitational waves from a binary system of black holes)
The rest is a matter of definition. We could define "feeling" gravity as perceiving its effects on our bodies. And the way we perceive the consequences of gravity on Earth is a sensation of the ground "pushing" upwards on our feet, and preventing us from freefall towards the center of the planet.
However, don't forget that gravity is basically curvature in spacetime. When you're in freefall, you simply follow a geodesic through the curved spacetime in your vicinity. In this sense, you can't "feel" gravity because there's nothing to be "felt" -- in the absence of other forces, your body is simply following a geodesic that is curved by the presence of a massive body (the earth).
If you were inside a free-falling box, you would never be able to tell whether you're in deep space (far away from any massive objects), or plummeting towards the surface of the earth. So, in this sense, gravity cannot be "felt."
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