Holy crap, I must be superman then cos I can empty my lungs and hold my breath for longer than 15s!
Try it in a vacuum. Or, rather, don't.
The problem isn't the lack of a new intake of oxygen.
As you say, a human can go longer than 15s without a new intake of oxygen. That is true because they will already have a considerable amount of oxygen in their body from previous breaths, even if they have just breathed out. There will be some air in their lungs because breathing out won't completely empty their lungs and there will be quite a lot of oxygen in their blood.
The problem is that the human body is very strongly adapted to at least some pressure. It doesn't have to be exactly the same pressure as you'd get on the surface of Earth, but it does have to be some pressure. With no pressure at all, the human body won't function correctly. Most importantly in this context, it won't do gas exchange. So it won't be able to use the oxygen that's still inside it - the remaining oxygen in your lungs will not be transferred into your blood and the remaining oxygen in your blood will not be transferred into the rest of your body.
If you breath out and hold your breath in an environment with enough pressure, you will have some period of time in which your body will continue to use the oxygen still in it, which will keep you alive and conscious for a little while, maybe as much as 3 minutes if you're very fit.
If you are in a zero pressure environment, you will suffer total oxygen deprivation immediately because your body will not be able to use the oxygen still inside it. Your brain will be affected immediately, as it uses a lot of oxygen. A partial shutdown will occur almost instantly and you will be unconscious in a matter of seconds. 15 seconds tops, probably less. On the one occasion when an astronaut training exercise went badly wrong and he was exposed to almost a vacuum without any protection, he lost consciousness after 12 seconds.
So no, you're not Superman. You just didn't have the relevant knowledge and you were wrongly assuming that the difference between zero pressure and air pressure at the surface on the Earth has no effect on human physiology.