Satire is offensive sometimes because it makes fun of someone or something. If it doesn’t make fun of something that is personal to the person, then they don’t feel offended. However, the topic of the piece may be offended. So, there is someone who is usually offended by a piece containing satire. That same person may not be offended with any other satirical piece.
This is why satire is often offensive. There may be only a few people who are offended by one piece of work that contains satire, so it is not a lot of people. The nature of a satirical piece is meant to offend. It is allowed because of the freedom of press and people will often use satire because they are not stating something directly to someone’s face.