Why is the tail so important that the plane crashes when it ripped off in the sky?

Without the tail there is still some control left to the pilots. The pilots can control yaw as well as altitude by varying power and directional control maintained with elevator inputs. This is more easy or difficult depending on the type of plane. However several crashes have been caused by problems in the tail including structural failures such as you described but the crashes were more a result of the catastrophic events that causes the tail section to fail. Examples include Japan airlines flight 123 and United airlines flight 232. However American Airlines flight 587 is an example where a failure limited to the tail section caused the aircraft to crash. The phase of flight (take off) as well as poor pilot inputs were the main factors that resulted in this being a non survivable incident