Did you read the article? It answers your question. Take a look at the section that begins with this:
The problem is called a paradox because two analyses that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first analysis argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money.
If you don't find this convincing, that's the point. Half the people who read this think one answer is obviously right, and the other half think the other is obviously right.
The problem is called a paradox because two analyses that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first analysis argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money.
If you don't find this convincing, that's the point. Half the people who read this think one answer is obviously right, and the other half think the other is obviously right.