Why is the opposite of plantar flexion called "dorsiflexion"?

Dors/dorsum in Latin simply means "back", and it is rather normal and reasonable to use the equivalent term in English with regard to the extremities (hands and feet), see "back of my hand".

It is medical convention to refer to the non-gripping surfaces of the feet and hands, as well as the upper (towards the brain) surface of the tongue as "dorsal".

My best guess for the etymology sequence is that all the terms were borrowed from Latin anatomical books written by Roman and Greek doctors (Dioscorides, Galen) which named the anatomical structures in normal language (back/dorsum, stomach/venter, sole/plantarum) and these terms were then fixed into modern medical terminology as jargon.

Caveat: I could not find any citation for the etymological sequence, but it seems a rather reasonable explanation to me.

Although the other 2 answers are accurate and well thought out, I just wanted to answer this with a bit different focused response.

Two things to note:

1. In general, one should think of flexion as decreasing the angle of a joint (see here, here, here, here, here, here or here for reference). From Saladin's 2015 Anatomy textbook$^1$:

   Flexion = a joint movement that , in most cases, decreases the angle between two bones.

   Put differently,

   Flexion refers to a movement that decreases the angle between two body parts.

2. As the other linked answers have aptly described, the superior surface of the foot is referred to as the dorsal surface (dorsum meaning "back"), and the inferior surface is referred to as the plantar surface (from Latin plantaris, from planta meaning "sole").

   

Given these two pieces of information, we can understand why the terms dorsiflexion and plantarflexion are used:

• Dorsiflexion = decreasing angle between dorsal surface of foot & anterior side of of the leg.

• Plantarflexion = decreasing angle between plantar surface of foot & the posterior side of the leg (or, more realistically, between the plantar surface and coronal plane of the leg).

From University of Michigan:

A transverse axis through the ankle joint allows a pair of actions similar to flexion and extension at the wrist joint.

The analogous action to wrist flexion is one that would tip the sole of the foot downward, increasing the angle between foot and leg. The usual term for the increase in such an angle would be extension, but in order to emphasize the relation between foot and hand, this action is instead termed plantar flexion .

The action similar to extension at the wrist would be a tipping of the upper surface (dorsum) of the foot toward the anterior surface of the leg. However, this would decrease the angle between the body segments, and action usually termed flexion. Since the term, plantar flexion, has been used for the opposite action, this is now referred to as dorsiflexion.

$^1$ Saladin, K. S. 2015. Anatomy & Physiology: The Unity of Form and Function. Seventh ed., McGraw-Hill, New York, NY. 1248pp.

In the same vein, why is the top surface of the foot called the "dorsal surface?"

I don't think the above answers are correct -- they do not really address the question of why the top of the foot is the dorsal surface, and why the surface of the hand opposite to the palmar surface is dorsal.

The reason why the top of the foot is dorsal is due to how the body develops embryologically. See the below figure:

Figure taken from Dr. Ann-Judith Silverman's human development notes, Columbia U. See: Human Dev Notes

The dorsal side of the upper and lower extremity begin on the dorsal/posterior surface of the body. However, during the 6-8th weeks of development, both the upper and lower extremity will turn medially, so that the originally dorsal surface is now anterior/ventral.

The position of the human foot by human anatomical convention dictates that the human foot is perpendicular to the human body in a standing position, such that the rest of the human body (including the hands with the palmar surface facing forward) , but except the foot, will conform to the anterior or ventral plane versus the posterior or dorsal plane. The foot, at conventional anatomical position will have its own plane, consistent with the same reasoning such that the top of the foot is the dorsum, while the underside is the plantar surface (more correct), or the ventral surface (less acceptable due its confusing orientation).

The plane of reasoning for the entire human body at anatomical position above ends at the distal junction of the tibio-fibula with the tarsal bones, such that the human feet will have its own surface plane directly perpendicular at 90 degrees to have its own 'dorsal' and 'ventral' surface.

The feet as such is in a special position compared to the rest of the human body's plane surfaces to warrant its own. Thus by convention, one may acceptably hear 'antero-flexion' or 'dorsi-flexion' of the foot, but not 'supero-flexion of the foot' which sounds sort of disagreeable.

The same way, oppositely, it is customarily said the 'plantar-flexion of the foot' which is more accurate (rather than infero-flexion or ventro-flexion or postero-flexion of the foot which sounds quite confusing)