I guess, when I've given training lectures or similar, after some tuition in presentation, I play a role to be as well to be confident in that situation
Personally, I have a slightly different take on this. I don't see myself as playing different roles in different contexts, rather expressing different aspects of myself.
The presentation example is a good one. I'm an introvert, but for more than a decade was a qualitative researcher. So a significant chunk of my job was presentations (pitches, and presentations of findings), and an even bigger chunk was moderating focus groups of 8-10 people with, typically, at least half as many people viewing from behind the one-way mirror. I also frequently spoke at conferences to, typically, audiences of a few hundred.
So that was a job in which I had to be 'on' or 'up' for significant chunks of time. The rest of the work, however, was as introverted as you can get: sitting in a room by myself analysing all the things we learned, and putting those presentations together.
Initially, I thought of the 'up' time as playing a role, and the 'down' time as being myself. But as time went on, I realised that both were me – they were just different aspects of me.
To bring things back to tango ...
In my experience, most tanguer*s are introverts – and I don't think that's coincidental. It's a dance in which we can invite someone wordlessly from the other side of the room; spend 12 minutes with them without having to say a word; where we can express any emotion (not just the exuberance of many dances); and where we can dance with someone we've never met before and will never meet again.
The learning side of things, too, seems tailor-made for introverts. It requires intense work, including plenty of solo practice. It requires an analytical mind (
maybe more so for leaders, but maybe not – a lot of the analysis needed concerns technique, and followers generally need better technique than leaders as the dance is more technically demanding for them). It requires the ability to doggedly persevere at something for very limited reward for a significant time – the epitome of deferred gratification, at which introverts tend to be better than extroverts.
The extroverts in tango make more noise (naturally!), but I'd say we have them outnumbered!