Azizi, since you asked about other cultures, here (France) we make eyes contact with anybody we know, it means "I want to/I can talk to you". Then we avoid eyes contact with any stranger we don't want to talk to/be addressed by and this is why women avoid eyes contact with unknown men in the street as Maeve reported about Italy. It's also why when we hate/don't like someone we avoid eyes contact, it means "I don't want to speak with you"

When talking we usually expect people making eyes contact because it shows they're interested by what they're being told. Eyes wandering around surely say "I don't care about what you're saying, I don't want to listen to you" and this is why you can hear parents or teachers say "Look at me when I talk to you!", usually when you ask children about some mischief they did. But… we expect them not to stare when we tell them off because it means challenge and no shame. In such a dominant/dominated situation, I think it's the same attitude as the dominant dog staring the other dogs of the pack while these lower their heads and eyes (maybe it's what/when all this "lowering your eyes = respect" goes back to).
Avoiding eyes contact when talking is felt as a sign you're lying unless it'd be you're ashamed/shy/afraid (which sums up to the same lower position), it depends on the context.

Hope it helps. Next thread could be "Smiling at people"!