Why is the charge naming convention wrong?

It's not a mistake, and conventional current is not wrong or backwards.

Electric current is often thought to be a flow of electrons, but this is wrong. Electric current is a flow of electric charge. Charge can be positive (protons) or negative (electrons), and both types of charged particles can and do flow in electric circuits:

• In metal wires, carbon resistors, and vacuum tubes, electric current consists of a flow of electrons.
• In batteries, electrolytic capacitors, and neon lamps, current consists of a flow of ions, either positive or negative or both (flowing in opposite directions)
• In hydrogen fuel cells and water ice, current consists of a flow of protons.
• In semiconductors, the current can consist of holes, which are not quite the same as an absence of electrons.

(The Hall Effect can be used to show whether a charge carrier is positively charged and flowing in one direction, or negatively charged and flowing in the other.)

When a Lithium-ion battery discharges into a load, for instance, there is no electron flow in the battery, but there is still a current flow:

(Source: Center for Sustainable Nanotechnology)

If you considered only the electron flow, your calculations would be wrong. You need to consider the net flow of charge, no matter what the charge carriers. Conventional current abstracts away the different charge carriers and represents all of these different flows as a net flow of (positive) charge, simplifying circuit analysis.

Conventional current is not the opposite of electron current, so if they were defined to flow in the same direction, it would be even easier to confuse them and go through life misunderstanding what current is. Electron current is a subset of conventional current. Conventional current combines the effects of electron, ion, proton, and hole flows all into one number.

Wikipedia agrees:

In other media, any stream of charged objects may constitute an electric current. To provide a definition of current that is independent of the type of charge carriers flowing, conventional current is defined to flow in the same direction as positive charges.

The labeling of one polarity of charge as "positive" and the other as "negative" is totally arbitrary. It could be done either way and everything would still work out the same. Franklin didn't choose wrong; he just chose. Labeling protons as negative and electrons as positive wouldn't change anything. It might actually make things more confusing, as described in Ben Franklin should have said electrons are positive? Wrong.

If Franklin had instead chosen the electrons to be positive, then we might never confront the real problem. If electrons weren't negative, we'd easily ignore our misconceptions, and we'd end up with only an illusion of understanding. Yet also we'd still have all sorts of niggling unanswered questions caused by the misconceptions. Fortunately the negative electrons rub our noses in the problem, making our questions grow into something far more than just "niggling!"

(Someone resurrected this oldie in the queue, so just to be a contrary voice...)

Ben Franklin did get it wrong. He had just developed a remarkable new theory of electricity in which positive (+) and negative (-) had specific and accurate meanings, and he was unable to apply the two labels in the way he intended.

In Franklin's time electricity was thought to be composed of two fluids, "vitreous" and "resinous", that annihilated each other when they came into contact. Franklin's clever idea was to realize that the two-fluid theory was redundant, and that a single fluid flowing through metals would suffice. This led him directly to an analogy with water pressure or air pressure, in which a single fluid flows from the end of a pipe that has positive (+) pressure, and towards the end with negative (-) or vacuum-like pressure.

The problem was that Franklin had no way to separate the fluid from the metal to tell which way it was moving. He could make sparks, sure, but the fluid (electricity) moved so incredibly fast that nothing accurate could be discerned from watching them.

It was only with the invention decades later of the Crookes tube that it became possible to tell the direction of flow of this mysterious electrical fluid, specifically by watching the shadows it cast on the inside of an empty tube. Only then was it realized that the fluid that Franklin postulated was moving from the "negative" pressure side (-) to the "positive" pressure side, (+). But it was already too late. Decades of papers and textbooks using Franklin's theory and conventions had already been written, and it would have been a nightmare to attempt to flip the convention at that point.

We now call these particles of electrical fluid "electrons," and they do indeed behave very much like the fastest and most nimble fluid imaginable. For the most common way to convey this fluid, via metals, it is the negative terminal of a battery that creates a positive pressure (or voltage) to push the fluid outward, and it is the positive terminal that creates a negative pressure to pull the electrons back in.

(This similarity also explains why using analogies with water pressure to explain voltages and electrical flow can be a lot more insightful than one might expect. Both really are examples of fluids under pressure, even if the terminology is different and the analogy is incomplete due to electrons having the ability to do things that material fluids cannot.)

So, bottom line: Franklin clearly would have labeled his own choice an error if he had had access to better data, so I think we can too.

Central to this discussion is a common and widespread misconception: the wrong idea that electric current is a flow of electrons, and that flows of positive charge are impossible.

Nope and nope.

Only in metals is an electric current a flow of electrons. Protons can flow, and so can ions of both polarities. The type of charge-carrier depends on the type of conductor: metals, electrolytes, ionized gases. So, Franklin may have been "backwards" about way metals conduct a charge flow. But he wasn't wrong about proton conductors and PEMs used in solid-electrolyte fuel cells. Franklin was also wrong about battery acid and neon signs, where the moving charges have opposite polarities and flow in opposite directions. In Franklin's terms, electrolytes contain two (or more) kinds of 'electric fluid,' not just one.

In fact, when you get shocked by a HV power supply, no electrons flow through your body. The voltage impressed across your flesh produces a flow of the ions commonly found in your tissues: positive sodium and potassium ions, and negative chlorides, each polarity of ions flowing in opposite directions. How then can we describe the amperes which are electrocuting you?! Easy. Just use Conventional Current. That's what it's for. (Hint: ammeters measure conventional current. They do not report the percentages of positives and negatives drifting in opposite direction within the circuit.)

It's really quite amazing how many authors seem to believe Franklin's discredited one-fluid theory of electricity, or believe that electric currents are somehow "made out of electrons."

Conductor examples:

Metals - yes, electrons

Semiconductors - electrons in two energy bands (lower band is vacancies or 'holes')

Plasma - electrons, positive ions, negative ions (if Hydrogen plasma, then H+ bare protons are part of the current.)

Distilled water - protons (H+ ions) and OH- ions, no electrons

Battery acid - protons (H+ ions) and SO4- ions, no electrons

Oceans - Na+ ions, Cl- ions, some H+ and OH-, no electrons

Human flesh - Na+ ions, K+ ions, Cl- ions, many misc ions, no electrons

I suspect that WW-2 military training manuals are partly to blame for this situation. For instruction of technicians, their authors concentrated on metal wires and vacuum tubes, and based their concepts on the over-simplified (wrong) idea that "electricity equals electrons," and that all positive charges were really just a case of missing electrons.