[PeterisP]

1) respiration is burning the food, but it's not burning all the food; "calories in" refers to calories absorbed, not calories put in your mouth; and the proportion between those two varies depending on all kinds of things, including e.g. gut microbiome and temporary changes to that due to various drugs; so if you strictly count calories put in mouth you still get a hard-to-measure variability in actual "calories in" (unless you put a respirator on the subject and measure it that way).

2) All other things being equal, changing "calories in" will make you lose/gain weight. The trouble is, all other things are not equal - simply changing how much you eat will significantly change those other things, it has an effect on your metabolism and eagerness for physical activity, thus directly affecting also "calories out" if you don't carefully monitor that and work to keep that stable.

3) All other things being equal, changing "calories out" will make you lose/gain weight. The trouble is, all other things are not equal - simply starting/stopping working out will significantly change your natural appetite, how hungry you are and how often you're hungry, and which types of food you have cravings for, thus directly affecting "calories in" unless you carefully track what and how much you eat everything and actually do keep that schedule exactly the same.

[squidfood]

Yes, this is a good partial list of all the "bigger sources of error" that I mention above!