No, you don't injure yourself because you don't listen to your body. You injure yourself because you listen to someone who paid $1,000 for the title of “coach,” wouldn't know proper clean-and-jerk mechanics if they slapped him in the face, and thinks it's a good idea to do heavy, compound lifts for time.
I've just described 9 out of 10 Crossfit “coaches.”
The only redeeming quality of MOST Crossfit gyms is that they are getting more people in the gym, doing more than just wasting an hour on a treadmill or elliptical. But the potential for injury is astronomical because, generally speaking, the attendees have so little knowledge about what they're doing that they don't realize how unqualified their instructors are. My advice to people wanting to give Crossfit a whirl is to get some real instruction from a legitimate strength coach, learn how to move under tension, correct any strength imbalances and functional movement deficiencies you have, and then scale your Crossfit workouts yourself.
.