The failure to perform a task based not on a lack of skill but a lack of willpower or courage or possibly due to overwhelming fear. Usually this happens at the last moment possible and without any sort of alternative plausible excuse.
John was going to ask that hot girl out but he bitched out at the last second and walked away awkwardly.
Alex bitched out of the fight after he saw his opponent was clearly bigger
Person A: there's no way that girl is going to bungee jump
Person B: yeah I'm betting she is going to bitch out