Because it was the common sense decision.
Bragg can absolutely be criticized for his initial deployments - his cavalry was deployed so poorly that he fell for the Federal deception efforts and dismissed the main crossings as feints. Once it was realized that Rosecrans was crossing south of Chattanooga, he made the choice to evacuate and rightly so. Bragg's position was untenable. If Bragg stayed at Chattanooga, Rosecrans' army would fall on the Western & Atlantic Railroad, effectively severing Bragg's lifeline. With Burnside in Knoxville and Rosecrans south of Chattanooga, the Army of Tennessee would be encircled.
Add to the fact that the Confederacy's track record at relieving sieges was very poor (Fort Donelson, Vicksburg, Port Hudson), Bragg absolutely made the right choice. Had his cavalry been better deployed, he even stood a chance to greatly frustrate Rosecrans' crossing of the Tennessee River and even attack Rosecrans' army while it was still divided.