I hope people realize that the reason breathing in makes you more buoyant is NOT because you are now lighter. You are, in fact, now heavier because you have added a certain amount of air to your body. When there is more air in a tank early in a dive, after all, it is heaver than when it loses air. The difference between having more air in the tank and having more air in your lungs is that the tank stays the same size, but your body (the chest area specifically) gets bigger with the air intake.
Archimedes' principle tells us that we are neutrally buoyant when our body (with all the equipment) weighs exactly the same as the equivalent volume of the water we are in. If we are neutrally buoyant and then expand our lungs by adding air, we are now larger, and because that additional air has little weight, we are now lighter than that larger volume of water. If we exhale, our chest area shrinks, we are now smaller, and we become heavier than the same volume of water.
Archimedes' principle tells us that we are neutrally buoyant when our body (with all the equipment) weighs exactly the same as the equivalent volume of the water we are in. If we are neutrally buoyant and then expand our lungs by adding air, we are now larger, and because that additional air has little weight, we are now lighter than that larger volume of water. If we exhale, our chest area shrinks, we are now smaller, and we become heavier than the same volume of water.