You Should Be Burning In All This Oxygen

Everything you are made of is fuel, and you are soaked in the oxidiser. Put the two together and energy comes out - that is all fire is. The reaction is downhill, it costs nothing to start, and it has a molecule of oxygen pressed against every living cell you own. It still does not happen at any speed worth noticing.

Not because you are mostly water, and not because nothing has struck a spark. Both of those are real, and neither is the interesting part.

Oxygen's ground state is a triplet: two of its electrons are unpaired and point the same way. Everything organic in you is a singlet, every electron paired off. Spin has to be conserved, so a reaction that would have to flip one is forbidden - and a forbidden reaction is not an impossible one, it is a slow one. It is one of the reasons the barrier between you and that reaction is high enough for organic matter to sit in an oxygen atmosphere for a lifetime. A match, a catalyst or enough heat still gets over it. That is why fire exists at all.

And your own cells get over it on purpose. Metal atoms carry unpaired electrons themselves, and a metal centre's strong spin-orbit coupling is what makes a spin-forbidden step allowed. The last enzyme in your mitochondria, cytochrome c oxidase, takes oxygen apart at a centre built from one iron and one copper. You are burning. Very slowly, and only where you allow it.

Sources, in the order the video uses them:
Oxygen's ground state carries two unpaired electrons with the same spin, by Hund's first rule - and the exact singlet-triplet energy gap, which is in the pinned comment - Wikipedia, "Singlet oxygen": https://en.wikipedia.org/wiki/Singlet_oxygen
Conserving spin would require a triplet transition state for a reaction with a closed-shell molecule, which is what prevents a direct reaction at everyday temperatures - Wikipedia, "Triplet oxygen": https://en.wikipedia.org/wiki/Triplet_oxygen
The plain form of the whole claim: triplet oxygen reacts only slowly with most organic molecules, which have paired electron spins - Wikipedia, "Oxygen": https://en.wikipedia.org/wiki/Oxygen
That the spin rule raises the activation energy and lowers the rate rather than replacing the barrier, and that strong spin-orbit coupling and transition metals are the ways around it - Wikipedia, "Spin-forbidden reactions": https://en.wikipedia.org/wiki/Spin-forbidden_reactions
The principle behind the payoff: because of a metal centre's large spin-orbit coupling, spin-forbidden transitions become allowed - Kim et al., PMC11212722: https://pmc.ncbi.nlm.nih.gov/articles/PMC11212722/
That cytochrome c oxidase reduces oxygen to water at a binuclear iron-copper centre, the two metals 4.5 angstroms apart, in one rapid four-electron step - Wikipedia, "Cytochrome c oxidase": https://en.wikipedia.org/wiki/Cytochrome_c_oxidase
That this site handles oxygen in its triplet state, where a one-electron reduction is unfavourable and a simultaneous two-electron reduction is favourable - PMC10194837: https://pmc.ncbi.nlm.nih.gov/articles/PMC10194837/

One thing we are flagging rather than hiding: no source we could open states the last three of those as one sentence. That the iron and copper are what let the spin turn over inside that particular enzyme is standard bioinorganic chemistry, and on our side it is an inference, not a quotation - the one paper that says it in a single sentence is behind a paywall. The video stays at the level the open sources support, which is why it names the metals and the principle and does not narrate the enzyme's mechanism.