Let's take the 4 horsemen: terrorists, pedophiles, drug dealers, and money launderers.
* If you weaken encryption, you can catch more terrorists. At the same time, the terrorists can track down their targets more quickly, and they might even find your personal identity and counter-attack directly.
* If you weaken encryption, you can catch more pedophiles. But how will you be able to protect their victims? With weaker encryption/security, pedophiles will be able to track down information on potential/previous/future victims much more easily. And witness protection becomes worthless.
* With weakened encryption, one can crack a drug trafficking ring wide open. On the other hand, you will not be able to protect your witnesses. Worse, a smart organized crime cartel might be able to crack the encryption used by the police; using the thus-obtained counter-intelligence to evade capture. Witness protection programs become that much harder too, if not impossible.
* Money launderers will also be less safe if encryption is weakened. At the same time, everyone else's bank accounts will be less safe too, allowing for new kinds of fraud to proliferate.