What matters is where the carbon comes from. Animals breath out carbon that they recently ate, and plants take it in and then they shed oxygen as they do photosynthesis. This had reached a stable plateau for the previous ~650,000 years - life had stabilized it between ~180-280ppm.
Burning fossil fuels brings carbon back out of the ground that had been sequestered there for millions and millions of years. Humans have added enough in just 150 years to bring it up to almost 400ppm - this means we have better insulation and the atmosphere loses heat less quickly than it did before we added the carbon dioxide.
The facts about this were quantified by the US Air Force at Hanscom Field right here in MA when they were designing heat seeking missiles. Carbon dioxide blocks a fairly broad piece of the infrared spectrum, but not all of it, and they had to figure that out. Water vapor blocks a smaller and slightly different part of the spectrum, and other GHG also have their own "signatures" in the part of the spectrum.
Most of the carbon in the atmosphere is carbon 12 and that means it comes from burning old plants - i.e. fossil fuels.