Whether dung (or wood, or anything else organic) is burned or decays, about the same amount of carbon is released back into th environment. Only difference is the speed at which this occurs.
By definition, such uptake and release of carbon is the carbon cycle. By itself, the carbon cycle is remarkably stable, about the same year after year.
The issue is one of the burning of fossil fuels, which are stored carbon that has been out of the carbon cycle for millions of years. It creates a net increase in carbon and the concentration in the atmosphere goes up.
You can argue about what problems, if any, the massive burning of fossil fuels causes, but you can’t argue it doesn’t lead to higher carbon concentrations. I measure CO2 regularly in my line of work and I’ve seen an increase in just a few years in my outside reference readings.