Why does a candle blow out when we blow on it? Our breath is 16% oxygen and only 4% CO2

You blow away the flame from its fuel source. If you would blow less hard the flame might burn harder because more air is supplied to the flame (similar to a Bunsen burner). Because normally the flame of a candle gets its oxygen through a convectional airflow generated by the heat of the flame.

The reason why the flame is blown away from the candle is because the air you blow towards it moves faster than the speed of the flame front. So the air you blow at it moves the flame away from its fuel source, where the flame burns out due to the lack of fuel.

Combustion is a gas phase reaction. There are two requirements to generate a stable flame. Firstly the temperature must be high enough to vapourise the combustible material (wax in this case), and secondly the temperature must be high enough to generate the activation energy needed for the reaction. Heat is needed because gas phase molecules of wax and molecule of air won't react unless they collide with enough energy to break the interatomic bonds in the molecules.

So when you look at the flame on a candle you are not seeing the solid wax burn. Instead the heat of the flame vapourises the wax then heats the vapour and the hot wax vapour reacts with oxygen to produce the flame.

When you blow on a candle you are simultaneously diluting the wax vapour and cooling it below the point where the wax and air molecules can react. As fibonatic points out in his comment and excellent video wax vapour continues to be produced after the candle is extinguished, but without a source of enough heat to provide the activation energy the reaction won't go. Applying a source of heat can restart the reaction and reignite the flame.

If you look closely at the candle flame, you will notice that the flame hovers just over the wick, but does not touch it. This is because the flame is boiling the wax, which becomes a vapor, which then burns. All of these processes are driven by the heat from the flame. As you blow on the flame, you moving it away from the wax and disrupt this process. Eventually, the chemical reaction (the flame) moves too far from the fuel source (which is no longer boiling as quickly) to sustain itself.

Note: while the candle wick itself does burn, the vast majority of the light and heat in the flame comes from the burning of the wax.