(Supernews doesn't seem to be registering my 3 PM EST reply just now--apologies for duplication if it shows up eventually.)
It makes no sense to take the absolute value of a quantity expressed in decibels--that's saying that there's no difference between, say, a 100X voltage amp (+40 dB) and a 40-dB attenuator (-40 dB).
The directivity is just |S12 * S21|, i.e. the effects at one port of a short-circuit load reflecting all of the signal backwards through the network. In decibels, it's
D = 20 log(|S12 * S21|). Symmetrical. No big mystery.
Cheers
Phil Hobbs