The nitrogen oxide $\ce{NO}$ exists and has an uneven number of valence electrons. This is "impossible". Why does it exist? Why is it not dimerized?
Nitrogen has 5 valence electrons and oxygen 6. Whatever your skill, you cannot get a noble gas configuration for both atoms in a molecule like $\ce{NO}$ .
Of course, $\ce{NO}$ dimerizes at very low temperatures. But why only at low temperatures? $\ce{H}$ atoms and alkyl radicals dimerize easily at room temperatures, and even above. Why is it so hard to dimerize $\ce{NO}$? Why is the bond $\ce{N-N}$ in $\ce{N2O2}$ so weak?
Edit : The following assumption has been published : "This question already has answers here: Why doesn't nitrogen monoxide dimerize? (3 answers)"
I regret to say that none of the three proposed references do answer the question : Why is the bond $\ce{N-N}$ so weak in $\ce{N2O2}$