Where is the sense in the Dai Li betraying Long Feng, their long-time boss who provided them with power and influence, as well as maintained order in Ba Sing Se for years, and even their homeland, in favor of a 14-year-old princess of an enemy nation whom they had known for maybe a few days?
It makes no sense. They betrayed their boss for a 14 year old girl they barely knew. And they basically had Azula in their hands, the Dai Li could have arrested her and had a bargaining chip to negotiate with Fire Lord Ozai. The decision made no sense at all.