Where energy is coming from during your workout is largely irrelevant to weight loss.
If you burn carbs rather than fat during your workout, then your body has no option but to turn to its fat stores to meet your energy needs for the rest of the day. If you burn fat during your workout, then those carbs are still available to meet those other needs. What matters for fat loss is the overall balance between calories burned and consumed over the ENTIRE 24 hour day.
To put things in context, most people burn 1300-1900 calories per day just keeping your natural body functions ticking over (known as your metabolism). While even a vigorous workout only burns a few hundred calories.
The significance of exercise is not that it burns fat directly, but rather than it helps swing a calorie surplus (which would have you gaining weight), into a calorie deficit.
However, your co-worker does have a point (although his logic is wrong) - workouts over 30 minutes tend to lead to greater muscle wasting. As muscle burns calories even at rest, over time this lost muscle can lead to slower metabolism, and make your longer term weight loss efforts harder.
Unless you are training for an endurance event, once you can work out comfortably for 30 minutes or so, you are probably better off adding intensity to your cardio workout, rather than more time.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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