I too have always been very irritated by the technique books use of 2/4 for tango and the simple mathematics process leading to an incorrect tempo.
I found it made the exam more difficult having to remember how many times I had said "2" while concentrating on demonstrating a figure and counting "1 and 2 and 2 and 2 and ..."
Guests statement about "this important aspect of technique" has now led me to dig around a bit more and I offer the following for consideration:
I'm not convinced that counting in beats and bars is an important aspect of technique for a typical dancer. It makes no difference to them how many bars a particular figure occupies, they just need to be able to dance it to the music. Slows and Quicks make more sense and are much more useful.
A teacher/coach/choreographer may need to count beats and bars when creating a fixed length routine or trying to match phrasing but not otherwise.
I believe the root of the confusion lies in a fundamental difference in the way a dancer and a musician use beats and bars.
A musician starts by setting the tempo in beats per minute, then builds bars from there for ease of reading and referencing the music.
A dancer hears the music tempo in bars per minute, then breaks the bars down to fit in the steps.
I believe the early dancers heard the tango as 30-32 bars per minute. They were then told it was written in 2/4 time so allocated two slow beats to the bar.
I finish with some quotes from Henry Jacques "Modern Ballroom Dancing", 1944, which I believe demonstrates this early thinking and may explain the origin of the 1&2& count.
"A technical knowledge of music is by no means essential to the aspirant dancer. Indeed, many highly skilled amateurs do not know the first thing about it"
"In Tango there are usually two beats, although Tango music is very occasionally written with four beats to the bar"
"When counting in 4/4 time we usually reckon in "Slows" and "Quicks", each "Slow" representing two beats and each "Quick" one beat. Thus "Slow, Quick, Quick" would occupy one bar of music.
The Tango is not quite so easy for the novice to distinguish. Indeed, even to the expert a badly played Tango often sound like a Foxtrot. Even though there are only two beats to each bar, there is also a sort of echo to each beat. Thus when counting Tango Time we say: One "and" Two "and" to each bar. In my lessons on Tango, however, I shall use the simpler Slows and Quicks as well as the number of beats."
I must admit to following the guidance of that final sentance!