Because in the US (at least) if the victim won't press charges the police can't take action. And in a case like this the defence will attempt to attack the (alleged, at the time of the trial) victim's credibility, which can be devastating. It's the main reason why rapists so often get away with it. Also why gang members are hard to convict.

Some crimes don't have a legal victim, e.g. murder (victim is dead) or so-called "victimless" crimes (prostitution, drug possession, speeding, etc).