If by fossil fuel you mean coal, why would this add carbon since it absorbed it when it was vegetation? Wouldn't it be neutral?
The earth stores carbon in three ways:
CO2 in the atmosphere
CO2 dissolved in the oceans
Carbon stored in limestone, coal and oil
CO2 levels have varied widely in earth's history. When there's a lot in the atmosphere, plankton and jungle grow and convert it to solids and a lot gets dissolved in the oceans. This takes place over millions of years and is a normal cycle.
Human beings have only been around for 100,000 years. We can't survive in some of the extreme conditions that are normal on the Grand Scale of things. We're actually pretty fragile in that sense, and are unlikely to survive, as a species, as long as dinosaurs did.
If we are pushing the atmospheric levels of carbon too high, we're doing it by converting the long term storage (coal, oil) into atmospheric carbon. You get a lot of gaseous CO2 from just a little oil.
That's why burning 1 million BTUs of wood, is carbon-neutral; the tree sucked CO2 out of the air and you're putting it back. You haven't taken any carbon out of the long-term storage.
1 million BTUs of oil adds to the CO2 in the air without removing it first like the tree did.
That is a simple version of the carbon cycle in earth's geology, not a liberal plot.
There is no absolute certainty that elevated CO2 levels in the atmosphere are caused by Man. There is no doubt that levels are rising faster than at any time geologists can discover (except for right after huge volcanic eruptions). If the levels get too high, this will be a worse place for people to live.