If you ask the question, how many figures exist in tango argentino, the answer will be zero. There are no figures at all! You can name the different combinations of movements by different words, you can repeat them in your training, you can build up the list of names, but you can never ever replace the live communication of bodies by rehearsed schemes. We do not dance figures. Our bodies react to the movements of our partners and the music. Some movements can be linked perfectly, so they are pleasant and often repeated, but nothing more.
A tangero who knows only figures resembles a companion who speaks only by pre-rehearsed sentences. He can pronounce them perfectly, but you will never have an interesting chat with him. Poetry, humour, creativity, fantasy are unavailable to them.
But this is not the only problem connected with figures. The tragedy lies in the fact, that one who dances figures does not need to listen to his partner. Why, if he knows perfectly what to do? The more diligent in training of dancing figures, the less space is left for the live communication, and the harder it is to unlearn only these rehearsed schemes.
It is much more useful to spend time by studying the mutual movements in a couple. There is a few of them, they are simple, they are the building bricks of any figure. If you know them, you can easily create the new figures together with your partner during dance itself.