What is the divine wisdom behind prohibiting the consumption of rats and mice?

It is not necessary to know the wisdom behind the prohibition of anything, for every ruling in Islamic law has a meaning and wisdom. Perhaps the prohibition of eating mice is due to them being among the noxious animals that are killed both inside and outside the Haram (sacred precinct), and that they are considered repulsive and not among the good things (tayyibat). Rats are a type of mouse, and therefore the ruling on their prohibition is the same as the ruling on the prohibition of mice in general.