All life on earth is based around carbon

Most of what we eat (which is mostly carbon) ends up being exhaled as CO2, and what we don't and ends up as poop gets eaten by bacteria and such and turned into CO2 then (or other stuff like methane, which still ultimately ends up breaking down into co2.) We're not taking any significant amount of carbon into our bodies from any source but our food.

And that's true the whole way down the food chain, all the carbon you get from eating a cow, the cow got from eating grass. If you eat, for example, a fox, the fox got it's carbon from eating a rabbit or squirrel or whatever which in turn got it from eating acorns and carrots and such. If you eat a tuna, it got it's carbon from a smaller fish, that got it from still smaller fish, down until you find something that's eating plankton.

And pretty much all of the carbon that made up that grass, oak tree, carrot, plankton, etc. came from the air, so from animals and such breathing it out.

And it just keeps going around and around the carbon cycle.

That's all pretty much a self regulating cycle, you don't really need to worry about reducing or offsetting what you're breathing, nature takes care of that pretty well.

The issue is that for millions of years, we've had a lot of carbon sequestered deep in the earth in the form of fossil fuels- coal, oil, natural gas, etc.

That carbon has been out of the cycle for a very long time, and within the last couple of hundred years we started burning a whole lot of it, releasing it back into the atmosphere, and for a lot of reasons, our environment isn't really able to do anything with all that extra carbon now.

So that's the carbon you need to worry about reducing and offsetting.

A lot of carbon offsets take the form of planting trees. Trees do ok at carbon sequestration because trees are made of carbon, and they tend to stick around for a while. You suck a bunch of carbon out of the air, turn it into a tree, and then that carbon isn't really going anywhere for usually years, decades, maybe even centuries depending on the species, the climate, etc. But of course we also cut down a lot of trees, so that's kind of a Sisyphean task to plant trees faster than they're being cut down elsewhere.

This is also all of course a big simplification, that leaves a whole lot out for the sake of keeping things simple.