Abundance of sulfur containing compounds in the air
The tarnishing of silver by sulfur is primarily due to hydrogen sulfide. Hydrogen sulfide is found throughout the Earth's lower atmosphere, and has many sources including the human body$\pu{^1}$.  

The amount of hydrogen sulfide naturally found in the air has been estimated as $\pu{0.11-0.33 ppb}$ ($\pu{0.15-0.46 ug/m3}$). Lower levels ($\pu{0.02-0.07 ppb}$; $\pu{0.03-0.1ug/m3}$) have been observed in some remote areas$\pu{^2}$.  

Although these are relatively low concentrations compared to many other trace gases found in our atmosphere, silver is highly reactive towards hydrogen sulfide and thus tarnishing of silver is a ubiquitous issue. Additionally, some tarnish results from the oxidation of silver by oxygen.  

Regarding your question about silver tarnishing from carbon, it's a matter of reactivity. The overwhelming source of carbon in the air is carbon dioxide, and methane to a much lesser extent. Neither of these gases are reactive towards silver nearly to the degree of hydrogen sulfide and oxygen.  

1) Toxilogical Profile for Hydrogen Sulfide and Carbonyl Sulfide, U.S. Dept. of Health and Human Services, November, 2016
2) Ambient Air Guidelines for Hydrogen Sulfide, CAS Registry Number: 7783-06-4, March 27, 2006