What is the primary disadvantage associated with the inductive method of criminal profiling?
I would argue that almost all methods of criminal profiling rely on the inductive method of logic - that is reasoning from how things have been in the past to draw general conclusions about how things will be in the future.
Deductive logic being defined by true premises not entailling a false conclusion is bulletproof but less encountered outside of the realms of pure mathematics.
Inductive logic is usually good enough to stake our lives on but can go wrong as with Bertrand Russell's famous chicken thought experiment.
However, inductive logic can actually have true premises and still have a false conclusion. Thus when we see that a string of murders occurred during the daytime, and we suggest that a criminal may be unemployed - this may be a strong or weak inference depending on other inferences we can draw.
So the obvious drawback is that no matter how profound our inferences we may still be wrong.
That may seem like a big enough probabilistic hurdle to abandon the whole process altogether - but that would be a huge mistake. After all, probablistic gambling with inferences is something we do every day. We may get into our cars and drive reasoning that because we haven't had a crash before, means we probably won't get into a crash this time around - however, with this inference we'll also use our seatbelts, make sure the car is in working order etc to ensure that our inference will not be proven false.
If we take this analogy further, the car ride is like an investigation. We can draw inferences whilst employing safeguards so that we may not 'crash' the investigation by drawing unsafe inferences.
Thus research and criminal profiling will not only use inferences from the past but will apply complex statistical analysis to ensure that the foundations upon which our inferences are drawn are as solid as possible. We can also refrain from condemning based upon one inference alone, there should be a multitude of inferences such that to deny the picture the inferences are painting, would take us beyond the realms of absurdity or probabilities vanishingly small.