Everyone was thinking in terms of physics (i.e. force). Einstein knew one part of that is maths, pure maths. Force is physics because of mass. But acceleration is geometry, its the shape of your trajectory and its maths.
Imagine a pipe which is horizontally fitted across a wall. Now water jet is flowing through it, inside of it. Now that wall is on a rotating base. You rotated the wall downwards. The pipe is inclined downward, water streams across downward.
Now imagine you have a torch light fixed to one end cap. You get a horizontal output of light. Now the wall is rotated downward, obviously the light will also stream across downwards.
The mass of the water or light did not matter. Because they are guided by the pipe and wall.
The same thing happens in the universe. The space is what carries mass, and it carries all physical phenomena including light. When that space itself is inclined (warped, rotated or receded or whatever) light would follow a curved trajectory just like any object of mass would. Space is what holds them, matter and light. Space curves under gravity.