There actually is a logic behind it, the explanation of which has been lost in the transition from QR&O/CFAO to CBI. The first thing to note is that Posting Allowance was originally designed as compensation for the disruption caused by relocation (e.g. the move itself, changing of schools, new community, new bank accounts, etc). It was never intended as reimbursement for expenses of any kind. In other words, it's extra money because we've made your life temporarily miserable. Furthermore, the old CFAO used to describe Posting Allowance as having two parts, each equal to one half month's pay. The first part was the member's portion (i.e. for the disruption caused to him/her). The second part was for the dependents (i.e. for the disruption caused to them). If there are no dependents, then no dependents have been disrupted; therefore, logic dictates that there is nothing to be compensated in that case.
Whether this is still appropriate today is another argument, but this is the reasoning behind the half month versus whole month differential.