Back in the day, it was very dangerous to have guests over for dinner (especially if you were an important person). There was a time when powerful people would kill each other to protect or augment their influence. A very popular method of killing someone involved inviting people, or being invited, to dinner. Back in those days, knives were pretty dangerous (relatively speaking), and if you invited someone over to eat, you had to arm them with a knife in order for them to eat. And since they're armed, they might be tempted to do something... not so nice. Apparently, a fair number of people took advantage of this back in the day, which really called for a new way to eat.
Eventually, someone came up with the idea to pre-slice the food in the kitchen, so that your guests would not need a knife. And therefore, you didn't have to worry about a knife fight at dinner.
Now, even though we live in modern times where people forget that knives are a kind of weapon, people still do not use knives at the table because it's tradition and a part of their culture.