It’s only impossible if you forget anything is possible. There is a possibility life exists on – or in, more likely – the Moon. It’s just so near zero that we round it off as impossible.
The main factors against life on the moon are: no solvents capable of self-replicating chemistry, nor life-suitable-elements of abundance and complexity for biochemistry, very low and inconsistent temperatures/pressures on the surface, common collisions with astral debris, cosmic and solar rays/radiation (both electromagnetic and particle) due to a lack of magnetosphere, and of course no sign via human observations.
Lunar life is possible, but highly unlikely.
The Broad Spectrum Life 