Pine shavings will work, but, yes they will take longer to decompose than wheat straw.
You can get as complicated as you want about composting, but it's basically organic stuff rotting. There are two basic materials used in composting, carbon and nitrogen. The closer you get to the right percentage of carbon versus nitrogen, the faster the process goes. But even if that ratio is way off, it will still happen.
Those microbes need it to be moist. You don't want it soaking sopping wet or the microbes can't breathe, but they do need a little moisture.
What essentially happens is that the microbes digest the carbon. They use nitrogen for energy. That's why you need a balance of carbon and nitrogen. While they are digesting that carbon, they do tie up some of the nitrogen. If there is a lot more carbon than nitrogen, they may tie up practically all the nitrogen in the area. But that is only temporary. By the time the composting is over with, all that nitrogen is again available for the plants. Composting does not use up any nutrients. The nitrogen is available at the end of the process, just not necessarily during the process. So I’d say your husband is partially right, there is a basis for what he said, but there is more to the story.
An added benefit to composting is that in some forms nitrogen can be leeched away by water. But composting puts it in a chemical form that is available for the plants but it does not leech away as easily.
You can use a lot of different things for carbon; wood shavings, straw, pine needles, shredded leaves, shredded paper, plant remains from your garden, even wood chips, many different things. There are several different possible sources for the nitrogen. Chicken poop is a great one.
Something that often happens, especially if you clean out your coop often. The amount of chicken poop mixed with the bedding does not provide enough nitrogen for composting, so the process can take a really long time. Many of us use a poop board to collect the poop under the roost. This not only gives almost pure poop which is great for composting, but it helps your bedding last a lot longer.