[upofadown]

>and it's important to know in order to stay safe?

I disagree with that. Before someone learns to turn a cycle, motorized or not, they have to learn to not fall over. So we tell them that they have to turn towards the direction they are falling. Once they master not falling then in practice there is nothing more to teach. They can easily generalize to adjusting the bike to any lean angle because the required motion of the handlebars is exactly the same. If we don't tell them about countersteering they will have no idea they are doing something different for steep turns vs shallow turns. They just have to establish a greater angle sometimes.

Back in the day prospective pilots were taught by having someone show them how to move the controls for each possible manoeuvre. These days the prospective pilot is first taught what the effects of the controls are. After that they are entirely responsible for achieving the required aircraft attitude using that knowledge. They are told to roll the aircraft to turn. They are not told that they have move the stick to the right for a while and then centre it even though that is something that would not produce a continuous turn in a car.

[dahart]

It's not my opinion that learning counter-steering is a safety issue, there's a reason that practically all motorcycle safety courses teach it, and that reason is outlined in the Hurt Report on motorcycle safety.

https://en.m.wikipedia.org/wiki/Hurt_Report

"28. Motorcycle riders in these accidents showed significant collision avoidance problems. Most riders would overbrake and skid the rear wheel, and underbrake the front wheel greatly reducing collision avoidance deceleration. The ability to countersteer and swerve was essentially absent."

Wikipedia's article on counter-steering with respect to motorcycle safety begins with:

"Even more so than on a bicycle, deliberately countersteering is essential for safe motorcycle riding"

https://en.m.wikipedia.org/wiki/Countersteering#Motorcycles

You're free to argue against it using logic and analogies to pilot training, but both safety data and public opinion don't seem to agree. I would counter that pilots are most definitely taught that pushing forward (up) on the yoke causes the plane to dive (go down), that is somewhat analogous to counter-steering. They are also taught that turning left causes a left roll.

But this didn't answer my question either - counter-steering is so-called because you steer counter to the direction of turn, which is true. Even if it weren't a safety issue, why would it be inappropriate to name it? It is a thing that's different in some ways from other types of steering; we should have a name for that. We have names for everything.

[upofadown]

> that pilots are most definitely taught that pushing forward (up) on the yoke causes the plane to dive (go down),

No, they are taught that pushing forward on the yoke causes the nose of the plane to pitch towards their feet. The result of that depends on the starting attitude of the aircraft. Think inverted flight as an extreme example. In exactly the same way, pushing on the right handlebar has results entirely dependent on the starting attitude of the bike.

Your comment about the roll is correct. That is an effect of a control.

[upofadown]

If people are not swerving enough then wouldn't we want to teach them to swerve?

I am pretty sure that I have answered your question. It's just a pointless distinction to make. Such pointlessness detracts from actual important lessons. Should we come up with a name for the "oversteering" used to recover from a turn (pro-steering?)? After all, if you don't do it you will be stuck in the turn forever. That would be dangerous.

[dahart]

> Should we come up with a name for the "oversteering" used to recover from a turn

Ignoring the reductio ad absurdum, then if you're referring to how you have to steer the handlebars further into a turn in order to straighten out, there is a name for that: counter-steering. :)