A dеtailed aссount of the subtlеtiеs and teсhniсalities that highlight the problеm, is a rеsеarch topiс by itself!
An attempt is made hеre to provide some brief discussion on epistemological arguments, without mathematical jargon or detailed phenomenology, which I am sure some would wish to complement or improve. I would welcome it.
There are a number of reasons which, when combined, can help us understand why we don’t see how to proceed in the endeavour of finding a good theory of quantum gravity and hence unify it with the other forces of nature. The main reason is the physically different structures of the gravitational force and the other forces of nature. When it comes to gravity, even the notion of quantum fluctuations of the fields is already problematic. While for the other forces of nature quantum fluctuations have meaningful interpretation and are relatively “easy” to calculate.
Another possible reason is, the tools we are using and the philosophy we hold on the notion of quantisation of fields, and that we try to push this philosophy to include gravity. This has been realised in the “old” approaches, in which attempts were made to construct perturbatively renormalizable theories of quantum gravity. They have all suffered from one or another shortcoming.
A successful quantum field theory allows us to do calculations, and extract sensible results which then can be tested against experiments. In the two main approaches to quantum gravity, string theory and loop quantum gravity, such testable calculations have not been possible to access experimentally, due to the large amount of energies required. So the results of these theories remain at best, at the present time, just theoretical speculations. But both these theories are still being developed and by no means they are, at this stage, completed theories of nature.