Gary Taubes is a science journalist who has stirred controversy in his writings about the FLT. We hope to explain what is going on here.
The FLT states that the change of energy in a system is the difference between energy going in and energy going out. This seems rather obvious. If we say that a person has gained weight, the FLT says that she has taken in more energy than she expended.
Let's label the statement "person has gained weight" as "A", and the statement "person took in more energy than was expended" as "B". The FLT says only that A is equivalent to B. They are the same. A means B, and B means A. The FLT allows us to substitute one for the other, because they are equivalent.
Here's an example of how the FLT applies, wherein Gary understands, but Don does not:
Gary: "I got fatter over the holidays"
Don: "Well, you ate more calories than you burned."
Gary: "Duh! I just said that!"
Gary: "I have gained weight."
Don: "That's because you took in more calories than you expended."
Aha! Don is now espousing the usual energy-balance hypothesis of weight gain. But the FLT says that we can substitute in the above. The same argument stated differently (yet equivalently) becomes:
Gary: "I have gained weight."
Don: "That's because you have gained weight."
This above illustrates why any invocation of the FLT in this context is a tautology; it's just a restatement of the proposition. It doesn't explain anything -- it asserts no causation. The FLT does not say A causes B, or B causes A, it simply says that these two statements are equivalent: A means B. When one asserts such a causation, now that is no longer the FLT, it is a hypothesis. Correlation (in this case, exact correlation) is not necessarily causation!
It may well be true that overeating causes weight gain, but there is another hypothesis available to us, what Gary Taubes has called "the alternative hypothesis": weight gain causes overeating. This reverses the causality of the standard hypothesis, and we have not violated the FLT either way (in fact, it may be the case that one, both, or neither hypothesis is true; that is why we need more rigorous studies.)
One of Taubes' often repeated examples of the alternative hypothesis is explaining growth in children. Children as they grow take in more calories than they burn and gain weight, but it's not caused by overeating. It's caused by growth hormones pushing raw materials into the body to construct tissues, which causes great hunger and provokes compensatory eating in order to maintain baseline metabolism. Growth drives hunger and eating, it's not the other way around.
If we want to find an explanation for weight gain, we must look elsewhere than the First Law of Thermodynamics for an answer.