What is the implication of not being able to balance the complete combustion reaction equation of methanol?

This question has been intriguing me since 10th or 11th grade. The teacher just told us about it but didn't get into the details of the why. Recently I asked a biochemist but couldn't get an answer. So I bring it here.


$$\ce{CH3OH + O2 -> CO2 + H2O}$$


is the complete combustion equation of methanol. But the problem is it can't be balanced. What is the practical implication, and significance of this fact?


*Side question:*


What is the mathematical reasoning behind the inability to balance the equation?




Here is the balanced eqn...


$$\ce{2 CH3OH + 3 O2 → 2 CO2 + 4 H2O}$$ 


 3

Mass is conserved, charge is conserved, ignore spectator ions until the end. If it is a redox reaction, begin by listing each active atom's reduction or oxidation, e.g., 


Mn(+7) + 5e to Mn(+2) 


Cr(+3) - 3e to Cr(+6)


and find the least common denominator (here, 15). That gives you the primary stoichiometry, here 5Cr(+3) (going to chromate) with 3Mn(+7) (coming from permanganate). Add the other atoms, slop in H2O, OH-, or H+, add back the spectator ions. Confirm the same number of each kind of atom on both sides. Try it out,


CuSCN + KIO3 + HCl to CuSO4 + KCl + HCN + ICl + H2O


[Cr(N2H4CO)6]4[Cr(CN)6]3 + KMnO4 + H2SO4 to K2Cr2O7 + MnSO4 +CO2 + KNO3 + K2SO4+ H2O


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