Consider the possible basic conflicts in fiction: man against environment, man against man, man against society, and man against self. In most plots the conflicts are between people. Even in Robinson Caruso and Castaway, tales of man surviving in isolation, the fact that the protagonist learned to survive on his own didn’t bring the story to an end. The goal was to get back to people, and in both stories contact with people brought new conflicts.
What causes the conflict between fictional characters is often simple. Typically character A and character B want the same thing, but they don’t want to share. This love triangle plot is played over and over again with competition not necessarily for the affection of a person but for a coveted prize, a position of power, or a piece of land handed down by the family. However, there needs to be another conflict, one of personality which keeps the two characters from compromising to work out this difficulty.
I am sure you have seen personality conflicts played out in real life before. One person is emotional, but sensitive and the other logical, but cold. One person is quick to take offense when another offers criticism, but the critique is meant to point out a problem that really does exist. A subtle war starts because one person perceives that another is getting the special privileges, which very well maybe true because people who treat others equitably are very rare. So a collision of characters can often be drawn from real life.
In fiction authors often play heavy favorites with characters, creating heroes with admirable qualities and villains that are evil simply because they are. However, intriguing antagonists have real personalities that cause them to want to block the hero from reaching the goal. The personality conflict in which neither one is the shining knight or the dragon makes the conflict more compelling.
Creating memorable conflict between characters requires also requires an understanding of modus operandi. MOs don’t just belong to criminals. They are the identifying methods that characters use to get what they want. If two clashing characters want the same thing, how they go about obtaining it separates them. This gives clues into the internal motivations so authors do not have to blatantly describe characters as “good” or “bad.” Modeling characters on real personality conflicts results in heroes and villains whose life like immediacy draws the interest of real readers.