Most people spend part of each day standing, and if they have normal anatomy their heads are over their heels in this position. Even sitting or lying down, the head is higher than the heels (if not over the heels). Yet the phrase "head over heels" is used in ways implying it is an unusual situation. How did such usage come to be, and why does it persist? Why is the more obvious "heels over head" not used?
The Oxford English Dictionary describes "head over heels" as a corruption of "heels over head" (my emphasis). The latter phrase it cites from 1400.
My own experience is that as a small child "head over heels" was the first term I knew for what was later called a "somersault".
The phrase is used to describe someone who has taken a tumble with so much force that their head follows their heels as they leave their feet and continue to roll forward. I guess as the head follows the heels in this kind of tumbling motion, a spectator would see head and heels in the described relation at some instant.
It's an exceptional condition because usually folks keep their balance and don't often fall into this type of accident or perform these kinds of acrobatics.
I usually hear this phrase as "falling head over heels", which usually describes a state of serious infatuation, as a metaphor for how quickly and helplessly humans get into this state. People do testify that they do "fall head over heels in love".
As a mishap or happy accident this happens perhaps even less frequently than taking a physical tumble, although seriously infatuated persons are known to take tumbles voluntarily and with gusto.
Steven Pinker writes
...over has more than a hundred distinct uses, including Bridge over troubled water, The bear went over the mountain, The plane flew over the mountain, Amy lives over the hill, Barney spread the cloth over the table, and The book fell over.
About head over heels he explains
the answer is that over can refer to a path of motion (as in The cow jumped over the moon), not just a location, so the smitten one is being depicted in mid-handspring.
The English expression head over heels is parallel to German Hals über Kopf (neck over head), the only difference being that in German the expression is a logical image for someone falling down head first.
If OED has no explanation why in English things are the other way round one can only guess. Perhaps it is not mere chance that German Hals (neck) and English heels sound very similar.
All the same one would suppose that the expression should be heels over head. Maybe the expression sounded better with the short head /hed/ before heels with the long i. And I often found that idioms can take a form that contradicts logic but idioms often don't care for logic.