The primary reason the Mars Science Laboratory (MSL), which carried the Curiosity rover, did not use airbag landing technology was that the heavier weight of the MSL made airbag landing technology impractical. The MSL is significantly larger and heavier than previous missions that successfully used airbags, such as the Mars Pathfinder and the Mars Exploration Rovers. The airbag system would not have been able to adequately cushion the landing or ensure a safe touchdown for such a massive rover.
Additionally, the complexity of deploying a more sophisticated landing system, like the sky crane maneuver used for the MSL, was deemed necessary to ensure a safe and precise landing on the Martian surface, especially given the rover's required mobility upon landing.