I agree. I used to be the guy who refused to take a day off, probably borderline exercise-addiction. Even if I felt like shit I would go warm-up and start to feel "better" and then lift. Did I get work hard? Yes. Did I get sore and tired? Absolutely. Did I make any gains? No, not really.
Once I started following a program and took one or two rest days per week, I actually started improving my lifts, and I don't feel so beat-up all the time.
Taking days off from training has also allowed me to start engaging in other activities outside of the gym. I don't feel dependent on training and lifting to feel "normal" or productive. It wasn't easy at first, but it has been well worth the growing pains.
Like others have said, test things out for yourself. Don't take anyone's word as the undeniable truth. I would suggest logging your workouts (not just weights/sets/reps, but mood, aches/pains, RPE) and start to look for trends. See if implementing some rest/recovery days improves your lifts or your attitude towards training. Best of luck!