Would arrow pushing explain the mechanism of these oxide reactions?

[adf89812]

TL;DR Summary: When is arrow-pushing useless?

I tried a lot of time to explain

2 KMnO4 + 3 H2O2 → 2 MnO2 + 2 KOH + 2 H2O + 3 O2.​

My work: $$\mathrm{MnO}_4+\mathrm{H}_2 \mathrm{O}_2->\mathrm{MnO}_3+\mathrm{H}_2 \mathrm{O}+\mathrm{O}_{2}^{2-}-$$

$$\mathrm{MnO}_4->\mathrm{MnO}_2+\mathrm{O}_2$$.

The rest of these, I think the logic is the same, but I don't know if I can't figure this out because I'm bad or the arrow pushing is useless in explaining these reactions.

$$
\begin{gathered}
1 . \mathrm{HO}_2^{-}+\mathrm{H}_2 \mathrm{O}_2 \rightleftharpoons \mathrm{HO}_2+\mathrm{HO}+\mathrm{OH}^{-} \\
\mathrm{HO}_2+\mathrm{OH} \rightleftharpoons \mathrm{H}_2 \mathrm{O}+\mathrm{O}_2 \\
2 \mathrm{KMnO4}+3 \mathrm{H}_2 \mathrm{O}_2 \rightarrow 2 \mathrm{MnO}_2+2 \mathrm{KOH}+\mathrm{H}_2 \mathrm{O}+3 \mathrm{O}_2 \\
2 \mathrm{HO} \mathrm{O}_2 \rightarrow \mathrm{O}_2+\mathrm{H}_2 \mathrm{O}_2
\end{gathered}
$$
$$
\begin{gathered}
\mathrm{O}_2^{-}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{HO}_2+\mathrm{OH}^{-} \\
4 \mathrm{O}_2^{-}+2 \mathrm{H}_2 \mathrm{O} \rightarrow 3 \mathrm{O}_2+4 \mathrm{OH}^{-} \\
2 \mathrm{NaO}_2 \rightarrow \mathrm{Na}_2 \mathrm{O}_2+\mathrm{O}_2
\end{gathered}
$$

1. $$(\mathrm{RO})_3 \mathrm{P}+\mathrm{O}_3 \longrightarrow(\mathrm{RO})_3 \mathrm{PO}_3$$
2. $$(\mathrm{RO})_3 \mathrm{PO}_3 \longrightarrow(\mathrm{RO})_3 \mathrm{PO}+{ }^1 \mathrm{O}_2$$

 

[Borek]

Arrow pushing is basically useful for organic reactions, for inorganics not so.