Question

Why do we consider F=O for massless objects ?....Any other reason except , Acceleration = infinite

Answer 1

As per classical mechanics acceleration will be infinite. We cannot give any other reasons.

The flaw with this kind of a reasoning is due to thinking the classical mechanics way. If you analyze the situation using relativistic mechanics, there will not be any infinite acceleration.
The particle will move with the speed of the light.

You cannot apply Newton's Equation (Classical Physics) to any mass-less objects, because, all mass-less objects (like photons) travel at the speed of light, and at that speed we use equations from modern physics (Quantum and Relativity).

Without any force, they will keep traveling at constant velocity. To produce acceleration (to change velocity) some force has to be applied. (Remember that you can only decrease the speed)

But we don't need to bother about that. As far as your syllabus is concerned, we need to study only classical mechanics.