Why are feminists always offended?

Because a premium is placed on the value of sensitivity in contemporary Western society. It's considered important to be sensitive, so if someone is upset or offended by something you've done, it's typically seen as your responsibility to apologize and make that person feel better.

In other Words, claiming to be offended is a way of exercising power and influence in social situations. Feminists use offense to influence people to behave in a way that's consistent with feminist values. For example, if a man refers to a woman as a "chick" at a party, and a feminist claims to be offended, then the other partygoers will expect the man to be sensitive, apologize to the feminist, and change his behavior going forward to avoid hurting her feelings.

In this way, claiming to be offended can be a useful tool to change or control the behavior of strangers without having to provide a rigorous explanation for why others should conform to the subjective, politicized expectations of a feminist.