It's not that most people want to hurt others. It's just that most people care only for themselves. Source: reality.
Now, we could quibble about whether people are more like to help you or victimize you and we could both be right. Or, we could observe that I'm correct about society functioning mostly because people don't mess with other people very much, you could chalk it up to friction and the lack of interest in others, and I will chalk it up to general back-ground good will.
As an example: a bowl of candy on Halloween with a “take 2 pieces only please” sign on it. Most people will only take 2. A few people will grab a handful. And one person will come along and take the whole bowl.
Therefore, the parent poster's argument is actually true, even if the median person believes themselves to be empathetic.
Edit: ever been at a long line for the bathroom at a big concert or sporting event? Or driven on the roads? There's always someone cheating, often making it more dangerous or painful to be that median person.