In modern English, we would say, "We're not laughing WITH you, we're laughing AT you." You should know that the concept of "humour" is only about 700 years old, so I suspect something has been lost in translation. I realise this is from an IELTS reading text, and perhaps Daniel's explanation is all you need. In respect to the reading text, my Slovak boss once explained to me how the funniest joke in English (yes, we've found it and you can look it up... and no, you can't use it in combat) makes absolutely no sense in Slovak. I suggest you focus on the general idea of the text and not worry too much about random examples - the quote from Aristotle was just part of the bigger idea.

Making fun of other people is a way of telling the world that you are better than the people make fun of... if you make fun of fat people, it's becaue you are not fat and you think you are better because of it. if you make fun of different races, it's because you are not that race and you think you are better because of it. I could you countless examples.

He also saw it as a form of malice toward others. This is a huge topic! Better take Peachey's advice!

i don't know how he was thinking.