So you are saying I should stop turning off my A/C and lights, since someone else would use that electricity anyways?
No they wouldn't. Aside from extracting electric energy from a reaction, one of the main differences between f. ex. a nuclear powerplant and a nuclear bomb is that we can control the speed of the reaction. This includes the option to produce less electricity when demand is lower (or when profits need to go up, but we can skip that for now).
Should I run my taps 24/7 as well, since someone else would be using that fresh water anyways?
No to this one as well, for pretty much the same reason. Water that doesn't get "used" stays in the pipes, so if you reduce your consumption then overall consumption drops as well.
What the parent means is that CO2 that is bound in trees will get released back into the atmosphere fairly soon after the tree dies even without human intervention, while the CO2 released
by burning oil/coal/gas would have remained bound for a long time if we hadn't extracted it.