it wasn't so much 'losing the argument' as 'the entire League being rendered irrelevant in an issue of great concern to them'.

Yeah... I can see why she'd be upset, definitely. And the Centauri and the Narn were clearly operating in bad faith. But at the same time, the Council did actually work as designed; the powers voted, including the League, and that's the answer they got. The way it's set up, with one vote for each of the major races and one for the League means that it's *always* true that they have to have half the major races on their side to get anywhere.