Long podcast, decent overview of some related biochemistry. I don't think he accomplishes what he thinks he accomplishes in refuting the Carbohydrate/Insulin hypothesis, but still worth listening too unless you already know this stuff.
He defines what he's setting out to refute here in the show notes;
The biochemistry and physiology of the carbohydrate/insulin hypothesis of obesity: insulin stimulates de novo lipogenesis (fatty acid synthesis), promoting the conversion of carbohydrate to fat; insulin stimulates lipoprotein lipase (LPL) and inhibits hormone-sensitive lipase (HSL) at adipose tissue, locking fat into fat cells; since adipose tissue lacks glycerol kinase, it cannot reuse the glycerol backbone of fats digested by lipoprotein lipase, and dietary carbohydrate is needed to provide the glycerol 3-phosphate that forms the backbone of newly resynthesized triglycerides.
Those were the days... lots of fun when a common meme in low carb was that you could eat any amount of fat, and not get fat, because the fat cells couldn't even store fat unless there was sufficient glucose for glycerol synthesis. Fortunately, as Masterjohn points out, glycerol can be synthesized from protein. Better to store that fat in the adipose than the liver etc.
For me--there isn't really a carbohydrate hypothesis, so much as an observation. People restrict carbohydrates, and they lose weight. Mechanisms are nice, but they don't replace the observation they're intended to explain. There's another observation--as Dr. Fung says, he can make you fat. Just give you some extra insulin on a regular basis. The hypothesis comes in when you connect the carbohydrate observation to the insulin observation, a fairly easy thing to do since carbohydrate is an important driver of insulin. But ask a type 1 diabetic whether insulin is a driver of carbohydrate intake. So we have observations, where two things can both seem to drive weight gain, and are in turn drivers of one another. It at the very least seems like a very honest mistake to make, if it was a mistake.
He makes the observation that fatty acid synthesis from carbohydrate is fairly low "unless you overfeed people carbohydrate," that's a paraphrase but I think an accurate one. This is reasonable, fatty acid synthesis is energetically expensive. There are pathways of fatty acid synthesis that downregulate oxidation of fat, so even small amounts can be of significance, I think it's enough to say that glucose and insulin decrease the oxidation of fat and promote its storage.
The bulk of his argument, from what I can tell, is that energy balance is largely decided on a cellular basis. If an individual cell doesn't "need" glucose, then it will be unresponsive to insulin. An overfattened cell won't get fatter on insulin's prompting. Cellular calcium, potassium, atp, yadda yadda yadda. Insulin signals the opportunity for the cell to feed, rather than the desire. As long as we're anthropomorphizing, I might as well ask why it would be wrong to say that insulin signals the opportunity for fat cells to expand and propogate, rather than making them desire doing so. If insulin merely gives me permission to get fat, rather than making me get fat, well, permission denied.