Why did Einstein say gravity isn't really a force?

Because in Einstein's general relativity, gravity isn't a pull at all: it is the shape of space and time. Matter and energy curve spacetime, and anything falling freely simply follows the straightest path that curved spacetime allows. The physicist John Wheeler put it in one line: spacetime tells matter how to move, and matter tells spacetime how to curve.

Einstein's clue was a thought experiment he started in 1907 about someone in free fall. Inside a falling elevator, you cannot tell that you are falling: every experiment gives the same result as floating in deep space, far from any star. That works only because every object, whatever it is made of, falls with exactly the same acceleration. So the weight you feel right now isn't gravity dragging you down. It is the chair or the floor pushing you up, knocking you off your natural free-fall path.

Gravity doesn't vanish completely in free fall, though. Two objects falling side by side drift slightly toward each other, because both are heading for the centre of the Earth. Those small differences, the same ones that raise the ocean tides, are the real fingerprint of curved spacetime.

A theory this strange had to earn its place. Newton's law left Mercury's orbit swinging round 43 arcseconds per century more than it should, and astronomers even invented a hidden planet, Vulcan, to explain it. In 1915 Einstein's equations accounted for the drift with no fudge factors. Then in 1919, two expeditions photographed stars beside the eclipsed Sun and found their light bent by about twice what Newton's gravity predicts. Einstein became famous almost overnight.