Because, since they move at the speed of light (obviously), any rest mass would be infinitely increased, due to their speed.
Now, you might speculate that the speed of photons differs ever so slightly from the theoretical c, so that an almost infinitely small rest mass is now increased to a very very small mass, but we would then be able to correlate the bending due to gravity with kinetic energy released when a photon strikes an object, like with any other moving object. This is not the case.
Finally, experiments have shown that photons retained moving in a gravity field do not show cumulative deflection, something that would be the case if gravity (or some other force) was acting on them.
Hence the conclusion that space itself curves.
ETA: There is other evidence, but this should suffice.
Hans