Why are long oxygen chains unstable?
The top of the p block is unusual in the atoms being so small they can readily form strong multiple bonds, because (from a VB point of view) they can get close enough for good side-by-side p orbital overlap.  Hence they prefer to form multiple bonds if they can, and both N and O can do that to form diatoms.  So extended chains of either N or O atoms are generally less stable than a collection of N2 or O2 molecules.  Or if you have extra capping atoms around, like H, then a collection of N2/O2 plus some H2O/NH3, et cetera.

Carbon is the exception because it has four valence electrons, and a quadruple bond to form C2 is too high energy.  (From a VB point of view, there are no valence atomic orbitals left to overlap to form the 4th bond.)  The next smallest molecule it can form with itself with lots of double bonds is buckminsterfullerene (C60).  So without another element around, a long chain of O atoms can form a more stable collection of O2 molecules, while a long chain of C atoms can't form anything more stable at all.  (When other elements are around, all bets are off: long chains of carbon tipped with hydrogen are notoriously unstable to CO2 and H2O if there's plenty of oxygen around.)