Why is light affected by gravity?

Hint: In order to solve this question, we are going to first see how the light travels in the space, then, noticing the pattern of light along with the patter that the gravity follows in affecting any objects. After that we can explain how the light and the movement in its path gets affected by the gravity.

Complete step-by-step answer:
The theory of relativity states that the massive objects warps the spacetime around it. While going from one point to the other, the photons take the shortest distance, the light appears to be bent through the warped spacetime of a massive object. This means that the gravity does not directly affect or bend the light but it is the spacetime around the massive object that is warped due to the effect of the gravity. Then, as the light takes the shortest path, it seems like it is the gravity that is affecting the motion of the light. It can be concluded that although photons have no mass, it is also true that we see light bend around sources with high mass due to gravity. This is not because the mass pulls on the photons directly, but instead because the mass warps the space-time through which the photons travel.

Note: Alternatively, we can also approach this fact by considering that the Light always travels in a straight line by itself. But the presence of any celestial object curves the path of light. Since the way of light itself is affected by gravitation, the real source of gravity can't be mass. Thus, the photons, even after being massless, are affected by it.