First, the title should be "Why should blackmail be illegal?"
Second, the answer is: because you have the right to keep secrets, and you should not have to pay someone who happens to learn one of your secrets in order to continue to exercise that right.
[EDIT] You have the right to keep certain secrets, like your bank account number or your sexual preferences, but not your criminal activity. So blackmailing someone by threatening to out them as gay or exposing an extramarital affair should be illegal on the grounds that you have the right to keep those things secret, but blackmailing someone by threatening to expose criminal activity should be illegal on the grounds that helping to keep that secret makes the blackmailer an accomplice to the crime.