It's interesting that so far the responses indicate that there doesn't appear to be a motive or 'goal' behind this, as if it's something people 'just do'.

I see that like myself, one other (MickeyCheeky) has questioned it and like me, doesn't feel the need to do it.

It's so difficult for me to understand. Perhaps this is made much worse right now in my severely depressed state.

I see it mentioned that it's people just being nice but in my gloomy world, the nicest thing people could do is leave me alone.

We do things as a result of our thoughts and feelings, so can anyone that does greet strangers elaborate on their feelings in any way, though, please ?

I would address one if I was lost or had an emergency, for example, so I could end the following sentence in this way:-

I ask a stranger for directions because....I am lost and I feel worried that I will never find my destination.

Similarly, please could others complete this sentence for me:-

I say hello to a stranger passing me because....