When the tiny island nation of Malta voted to allow divorce in 2011, Melody Alan realized that her own strongly Catholic country, the Philippines, was the only one left in the world without that right (aside from the Vatican). Last fall, as the #MeToo movement began to ripple out from the U.S., she and fellow advocates for divorce seized the moment and tried to recast the debate.
Ms. Alan’s own husband left her and their two children for another woman in 2010. He offered to support an annulment of their marriage (an elaborate...