system
Given the following post, respond as if you're commenting on Reddit:
human
How does "Calorie-in - Calorie-out" and "You only burn fat after x Time of Exercise" fit together?

I often learned that we only burn fat, and thus loose weight, after 30 mins or so of exercise. (Because before that the body uses some other energy source).
Then the same people tell me, that the only thing that counts is the Calorie-in / Calorie-out balance.
So at least for my brain these two assumptions won't fit together. 

If I exercise for just 20 min I might not burn fat but still use Caloriens, so later in the day my body should rely on the fat as an Energy source.
So I might not burn fat while exercising but, if "Calorie-in - Calorie-out" is true, I should still loose weight.

This question is bugging me for years and all people I talked too, including my Sports Teacher, just keep repeating the thing about the energy-sources, and completely miss my Point. So I hope the question was clear enough and you can finally enlighten me and / or show me where my thinking error lies.
gpt
Calories in calories out (cico) is like a budgetary point: losing weight means burning more calories than you consume.

Burning fat after x minutes of exercise is just a comment on your body switching from primarily carb power (glycogen) to primarily burning fat (ketones) for fuel.  This distinction is not really relevant to casual exercisers or dieters.

To illustrate: A lb of fat is 3500 calories. So to lose a lb of fat a week you need a calorie deficit of 500/calories a day.  You can have a 500/cal deficit without any exercise or without exercising for greater than 30 minutes. In other words, your body also burns fat stores when you eat at a caloric deficit, otherwise no one would lose weight from starvation.