I recently had rotator cuff surgery and now I'm in physical therapy. At every session the therapist asks "how would you rate your pain today on a 10 point scale?". They tell you that 0 is "no pain" and 10 is "the worst pain you can imagine".
How am I supposed to answer this question? It always hurts. Some days only a little, some days a little more, and some days a lot. How am I supposed to tell the difference between a 3 and 4? I've never actually said anything bigger than 5. Does that mean that my 5 is really a 10 because it's the worst pain I have or is my 5 really a 5 because I can imagine much worse pain (being skinned alive, dental drilling without novacaine, etc.)
I'm not saying that there is no such thing as ordinal data. Many phenomena of interest are naturally ordinal (good, plus good, double plus good!). The problem occurs when we impose a numeral-based scale on an ordinal phenomena. People start to think that the numerals represent real numbers. Then they think it makes sense to analyze them as numbers: "The patient's average pain this week was 3.428."
Fortunately, my therapist has never made a statement like that, but course evaluations where I teach are done on numeral-based ordinal scales and every semester the institution computes means and standard deviations for teachers, classes, divisions, etc. It's statistical nonsense.