It means easily capable of growing angry, but as J.K. said, it seems to apply only to individuals. Although applying it to a relationship feels unusual to me, I cannot say why it would be wrong. Certainly people would understand what you meant. We do talk often of "angry", "hostile", "bellicose", etc., relationships. Instead of saying the relationship was irascible, I would say something like:
"in a split second it would turn to anger".