This is the one right everyone hates, but it is probably the most important right we, as humans, have. I saw a blurb about an upcoming story about a man who, apparently, intentionally ran over a box of kittens. This offended me. A lot. If I had been there, and had a gun, I might have shot the creep, and not lost a moments sleep over it later. Guess what though, I didn't run off to PETA with a donation, nor did I demand a boycott of anything this man had ever been associated with.
I was offended, but I didn't demand someone else make it better.
I support a lot of things, including the rights of individuals to do whatever they want without their neighbor interfering with them. By neighbor I mean everyone, including the government. Government should be about being good neighbors, which means that we all have the right to be offended. It does not mean we get to tell our neighbor how to live his life, or how to use his property.
I know somebody read that last sentence and just thought 'I bet he doesn't want a slaughterhouse to move in right next door.' Guess what, you are right, I don't. The funny thing is, that never happens. People that run slaughterhouses tend to be good neighbors, and put them places where no one is around to be disturbed by the noise, and stench. That might be because they don't want to live next to one either.
The problem comes later when people want see the nice view the slaughterhouse has because it was built away from all the neighbors and decide they want to move in. These people are the ones that tend to be bad neighbors, and they demand the slaughterhouse close up shop and move because it offends them that people eat animals, and killing animals is always cruel.
You have the right to be offended.
You do not have the right not to be offended.