You're right, Elena, it probably is a cultural thing!
Of course, these conversations are just standard greetings, and we are not really talking about our state of health. When we are saying hello to friends, neighbours and colleagues, 'not too bad' often means exactly the same as 'fine'. It's just a polite response.
If you're interested in learning why British people behave as they do, I'd recommend a book called 'Watching the English' by anthropologist Kate Fox. She observes that British people respond to many situations by making comments along the lines of 'Well, I can't complain'. In this respect, we are very different from the more positive and optimistic Americans, for example. The 'not too bad' response is a typical example of this very British attitude.