Oxidation of alkenes with KMnO4
Your professor obviously wants you to consider the $\ce{C-C}$ bonds of the $\ce{C=C}$ double bond plus any $\ce{C-H}$ bond to either of the alkene carbons.

The first step in double bond oxidation by permanganate will always be replacing a $\ce{C=C}$ by $\ce{C=O + O=C}$. If you consider the double bond two bonds, then for each of those bonds each carbon atom gets one $\ce{C-O}$ bond to again give a double bond.

After we have generated the inital carbonyl, we can turn our attention to the other bonds the former alkene carbon has. Remember that aldehydes are easily oxidised to carboxylic acids while ketones are rather resistant to oxidation. The difference is the presence of a $\ce{C-H}$ bond in the aldehyde; permanganate can oxidise this to another $\ce{C-O(-H)}$ bond. This is the second part of your rule.

If accidentally the carboxylic acid species generated is formic acid, which has another $\ce{C-H}$ bond, this can again be oxidised to give carbonic acid. Since carbon’s oxidation state is maximal in $\ce{H2CO3}$, this is truly the end of the oxidation.