Woodley does not have the emotional attachment to the negotiations that BASSAs reps do. He can afford to take a dispassionate look at the negotiations, the options BA have, the support BASSA really has (as opposed to the support the tubthumping devotees claim) and decided whether or not a strike is winnable in the current climate.
Given that BA have many options, and BASSAs suport is nothing like as solid as they claim, he may well decide that a negotiated settlement that looks almost identical to what BA propose is a better outcome than losing a strike. BASSAs latest update reveals that there have been no negotiations of late and BA have flatly rejected BASSAs offers since 30th June. That doesn't look like the actions of a company that are scared by the unions.