What happened here seems clear. Obama killed the idea of aiding Syrian rebels through a bureaucratic two-step. First, he refused to approve the level of aid his top advisers wanted. Second, he obtained a finding that the lower level of assistance he was willing to provide wouldn’t be sufficient.
This doesn’t mean Obama’s decision was incorrect. Among other drawbacks, supplying Syrian rebels with the kinds of weapons Petraeus asked for is risky because we cannot be confident they won’t fall into the hands of Islamist extremists. I’m not even sure we can be confident that the “moderate” factions to whom we would be supplying the weapons don’t include Islamist extremists.
Obama’s clear mistake, in my view, was his failure to identify reliably non-extremist forces to support early in the rebellion, before the radicals, aided by outside extremists in al Qaeda, became ascendant.