Question

why photons don't have mass.

Answer 1

simply because they are the energy particles causes by the electromagnetic variations. or a number of particles doesn't interact with higgs field and the photon being one of them has no interactions with it leaving it massless. actually many reasons still remain but if you're looking for the short version this might do it but you can also do big study.

Answer 2

If photons said as energy then why they are consider as particles.
I mean both wave nature and particle nature.

Answer 3

they are considered to have no mass because their all mass is converted into energy

Answer 4

showing a particle nature does not necessarily mean that the mass is there. everything has dual nature if know from the debroglie's wave equation and photons are not an exception they are energy waves which behaves as particles as well. to be honest the thing about photons is not that easy and a way to explain it is the equations from e.m theory.