[Fomite]

So let's pretend there's three types of trees we want to study: Oak, Maple and Aspen, which we code as 0, 1, and 2 for reasons (there are some good reasons to do this).

Statistically, if you treat them as a continuous variable, the estimates you get will act like there's an ordering there, and give you the effect of a one unit increase in tree. So it will tell you the effect of Oak vs. Maple and Maple vs. Aspen, assuming those are proportional and that Oak vs. Aspen will be twice that.

This is...nonsense, for most categorical variables. They don't have a nice, ordinal stepping like that.