Bear with me for a moment:
If inertial and gravitaional mass are exactly equivalent, and a photon has momentum (granted, it is 4-momentum - so we are dependent here upon the frame of reference) and (crudely - and, you are going to say, incorrectly) momentum is mass times velocity, then from the fact a photon has momentum we can deduce that it has mass (p=mv). From Einstein's equations, however, we can deduce that it cannot have any rest-mass, as at speed-of-light (c) movement it would have infinite moving-mass.
BUT suppose - just for a moment - two heretical things: firstly that a photon DOES have rest mass (very tiny, but non-zero), and secondly that light does NOT travel at c - the upper speed limit for the universe - but very, very slightly less than that. We speak of c as being "the speed of light in vacuum" but we also speak of there being no true vacuum anywhere in the universe. Even intergalactic space contains some matter - per cubic metre not much, but some. So we have never - and I really do mean never - measured the actual speed of light in vacuum. We have measured the speed of light in "close to vacuum" (and in glass and in water and in air and lots of other media too), but never actually "in vacuum".
Still bear with me: so what if the rest-mass of a photon is, say ten to the fortieth power smaller than the mass of a neutrino (... when I was a child I was told neutrinos have no mass - but that's changed!), and that the maximum speed of light actually occuring in the universe is one ten to the fortieth part smaller than c (the ultimate speed limit)? Then we could still have Einstein (scientifically good) and we could think of photons as having mass (ordinary common sense good) and we can get rid of Black Holes (I've never liked them - but that, I know, is not a good argument) and instead have very, very deep (but NOT infinitely deep) gravity wells.
Photons are very light - but NOT massless. Photons always move at LESS than the (unmeasured) upper speed of light..
OK - you can stop bearing with me now.