I can’t recall my source, so I can’t vouch for the accuracy of the information, but what I’ve read about this subject agrees with the Cruiser aViation theory. Naval aviation initially had just a reconnaissance role, and so was regarded as an extension of the function of cruisers, one of whose jobs was to act as the scouts of the fleet. “CA” couldn’t be used because it was already taken to designate (I think) heavy cruisers, so rather than the first letter in “aviation” being added to “C”, the second one was used instead.
Still, there are other theories floating around. One creative explanation that I once heard – from a crewmember of the nuclear carrier USS Enterprise – was that “V” stood for “Vixed wing”, an alternate pronunciation of “fixed wing” which distinguished a fleet carrier from a helicopter-carrying assault ship. I don’t think he was kidding me, but I found the explanation a bit too convoluted to be convincing.