This is a fundamental question requiring fundamental thinking. I shall keep away from theories and concentrate on simple facts. From the day we knew of the Brownian motion and realizing that particles of matter are on a continuous motion and not at rest, we should have realized that motion and not rest is the true influential variable of nature. Velocity should therefore be adopted as the prime variable we use to study nature. But velocity has the units of space and time locked in an inseparable format, we should then conclude that space-time is a the variable that need to be considered in our scientific endeavor. But velocity of particles have to involve mass too. This then says that the most fundamental variable of nature is momentum with the units of mass, space and time locked together. As particles possess electrical charges too, we should also add electrical charge unit to get to the fundamental variable of nature.
When we look round we see that E.M radiation has all the above attributes. It has mechanical attributes in the form of energy and momentum flowing along the direction of propagation. This is given by the pointing vector P=E^H. Radiation also have electrical and magnetic attributes in its electric and magnetic fields that are normal to each other and normal to the direction of propagation. These attributes are all verifiable experimentally in the lab by simply directing a beam of radiation onto neutral and charged objects to see them move according to the laws of mechanics and electrodynamics.
That radiation is the fundamental ingredient of nature is supported by astronomical observations- which showed that radiation is all that is there at the start of the life of our universe. It is also supported by experiments in the lab wherein pure radiation(gamma rays) can produce matter, and pure matter(anti matter included) can produce pure radiation. The process is fully reversible and indefinitely. We can thus say that radiation could be considered as evaporated matter and matter as condensed radiation. If radiation condenses by going round (at the same speed) in closed loops, we get trapped radiaton, or rest energy or rest mass as a result. The circulation of the momentum produces the intrinsic spin, and that of the electric field(radial direction) creates the electric charge(Gauss theorem). The magnetic field vector is normal to the other two- producing the magnetic dipole moment along the spin direction. This completes all the required matter attributes- emerging as a result of radiation condensing into matter- thus supporting the radiation origin of matter.
Hence, momentum linear or angular is a defining property of our universe, be it in the form of energy or matter. As to why light bends round massive objects, we note that gravity also emerges when radiation condenses into matter. The key idea here is conservation of momentum. This is a fundamental property of our space and an experimental fact. Even elementary particles and radiation can't afford violating this principle. But if momentum is conserved, the forces between any two isolated particles locked in an orbit must be of the inverse square type as given in Bertrand theorem. Actually the theorem allows a spring type force(Hook's spring force) too, but this can be shown to be a limiting case of the inverse square force. Thus Newton's law of gravity and Coulomb's law of static interactions emerge as radiation condenses into matter.
Now, the formula for the bending of a projectile in the vicinity of a massive object in the Newton's theory(the inverse square force theory) have only the speed of the projectile in it, and not its mass. The mass simply cancel's out. According to this fact, Newton proceeded to calculate the deflection of light caused by the sun for example. As it happened, Einstein calculated the same angle and found it to be double that of Newton. People without deeper thinking announced that this meant that Newton's formula is wrong and the whole theory should therefore be discarded- despite the fact that the mass of the sun is not that of a black hole to merit a big modification of the Newton's theory. It turned out that Newton's calculation gives the actual angle of light deflection, whereas what we measure is twice that value due to the symmetry of the problem as shown clearly here; https://file.scirp.org/pdf/JMP_2017102615295175.pdf. The rays that are drawn straight from the source to the sun surface can't cross to the other side- they hit the Sun's surface instead. What we see is rays that come from an angle equal to that after crossing the Sun's surface. The two results support each other in a sense.