In Beowulf revenge was a quite common motivator. People were expected to avenge the death of a loved one by killing the person that murdered them. To refrain from doing so would bring dishonor on your family and brand you a coward which is the worst thing to be in their society. Nowadays people are expected to let the legal system do the work. If someone takes matters into their own hands then they will end up in prison too. Murder is wrong no matter what the reasoning behind it is according to our society. In Beowulf revenge is not really seen as murder. It is more of a way of honoring the dead. It shows that you cared enough about that person to avenge their death. Of course this is not the only difference between our societies. There is also the issue of modesty. In this society it is expected for people to be modest and bragging is frowned upon. In Beowulf telling everyone what you have accomplished shows your pride which is a good thing. Beowulf introduces himself by recounting his past triumphs. Whereas we would see that as him being cocky and possibly annoying it is completely normal to them.
The society in Things Fall Apart shows large differences as well. For instance whenever a set of twins were born they would be left to die. It was believed that twins were unnatural and would bring the wrath of the gods if left in the village. Of course to us this is barbaric and cruel but this is just because we were not raised in that culture. It is just a necessary evil in that society. They must sacrifice some for the good of the whole village. Also the men were allowed and encouraged to have more than one wife. Wives were basically status symbols. If a man could afford to provide for more than one wife the. They were clearly wealthy and deserving of respect. This is not necessarily wrong it's just different from our society. This highlights the basis of cultural relativism. Just because something is different that does not mean it's wrong.
