Specifically, the FBI wants us to make a new version of the iPhone operating system, circumventing several important security features, and install it on an iPhone recovered during the investigation. In the wrong hands, this software — which does not exist today — would have the potential to unlock any iPhone in someone’s physical possession.
I don't understand how there is currently no backdoor if building an alternate operating system would permit them access to encrypted data on this individual phone.
It sounds like the actual security at this point doesn't come from strong encryption, but from restrictions around the install of a new iOS. That is, an OS installed by Apple can circumvent encryption on the phone. This would mean that Apple does have a backdoor.
My guess is that a new install can remove the brute force protections.
EDIT: Here is a nice overview that suggests that because it is an iPhone 5C, this is possible, however, it wouldn't be with an iPhone 6.
If the San Bernardino gunmen had used an iPhone with the Secure Enclave, then there is little to nothing that Apple or the FBI could have done to guess the passcode. However, since the iPhone 5C lacks a Secure Enclave, nearly all of the passcode protections are implemented in software by the iOS operating system and, therefore, replaceable by a firmware update.