Question

Why we cannot light fire on the moon?

Answer 1

because fire need oxygen and there is no oxygen in the moon

Answer 2

As anyone who has ever been on a fire marshals' course [1] will know, you need three things to start and sustain a fire: 

fuelheatoxygen
If any of these are absent, you cannot start a fire. If you deprive an existing fire of any of these things, it will quickly extinguish. 

It's difficult to think what might be classed as 'fuel' on the Moon. It has no surface vegetation, and no hydrocarbon deposits in the form of oil, gas or coal (because it has never had a prehistoric biosphere, unlike the Earth). 

But even assuming that its entire surface was made of combustible material, and you applied a source of heat to it, in the form of a nuclear bomb, say (let's go for extremes here, as they more easily disprove the general case), and manage to momentarily 'ignite' those combustible materials, the fire cannot be sustained without a source of oxygen. 

There is obviously no atmospheric oxygen on the Moon, because it has no atmosphere. So the only oxygen that could be present is that bound in compounds in the minerals of the Moon's surface. I'm not an expert on the mineral composition of the moon, so I don't know how much oxygen-rich mineral deposits there might be. 

Even supposing you could liberate this oxygen with the heat of the nuclear bomb, it would quickly 'boil off' into space because of the Moon's low surface gravity, so it would not be around long enough to sustain the combustion of whatever materials you managed to ignite with the bomb. 

Taking all these factors into account, I think it is fairly safe to say that you could not 'set fire' to the Moon, because it is not made of readily combustible material and there is no source of oxygen to sustain the combustion.