A protagonist and an antagonist can be basically the same figure, walking down different roads.
A protagonist starts with a loss which grows bigger and bigger as the story moves on. Each idea, tool or action which he or she takes turns out to be wrong, or inadequate. Often the protagonist makes things worse by doing something which only serves to magnify the loss or emptiness. Thus Pip, in Dickens’ Great Expectations, decides to take up the offer to be turned into a gentleman in order to try to win his love, Estella, only to find that this transforms his life into a dwindling abyss. Each time Frodo decides to use the Ring in The Lord of the Rings, things get worse; Luke Skywalker sets out to rescue his friends in The Empire Strikes Back and loses his hand as well as his positive view of the world. What happens in the end is that the protagonist sees beyond his or her original goal. This often means a willingness to sacrifice themselves for something greater in the climax of the tale.
That sacrifice is what makes the difference.
An antagonist begins in most stories later down this road of decision-making. Instead of seeing behind their initial desire and confronting the sacrifice of self that needs to be made, though, the antagonist has gripped more tightly onto the notion that his or her decisions are correct. The antagonist has to be right, at any cost. This usually involves closing down his or her ability to perceive, hiding truth from themselves, stopping time, freezing the landscape, denying motion, fixing things in place which should be free. Miss Havisham in Dickens’ novel stops all her clocks and shuts the windows of her home to the outside world, irrationally determined not to move from the moment she was betrayed; Sauron in Tolkien’s epic shrouds himself in cloud and fails to see the flaw in his plans; the villains in Star Wars refuse to see, in their arrogance, that they have left themselves exposed. The White Witch in C. S. Lewis’s The Lion, the Witch and the Wardrobe literally freezes Narnia so that she can dominate it.
In this way the protagonist’s act of sacrifice takes advantage of that very gap or flaw or fault and brings the antagonist’s cold empire crashing down in ruins.