I view CAP theorem as statement about the universe we live in (information travels at speed of light, "instantaneous" is observer dependant etc), and not as a consequence of information theoretic definitions we chose to adopt (strength of consistency or availability). Yes, when stated simplistically (you have 3 properties C, A, P choose 2) can be extremely misleading, since you can't really choose P, you can only decide what to do in case of P. But like any mathematical theorem one has to understand the preconditions when the theorem applies, understand the various computing model assumptions etc. to actually use it.

Notwithstanding, I still find it very useful as a general guide when designing distributed systems.