I imagine it is because a photon can't be stopped. The speed can be reduced a little bit if it passes through something with a certain index of refraction, but that is a special phenomenon. Also, the speed remains constant even in the object with a certain index of refraction.
You won't be able to reduce the speed to 1 m/s or anything really low. Therefore, it doesn't have a mass.
Also, light passes through itself. There is no such thing as a head on photon-photon collision.
There probably are better explanations in physics books.