Don't say that a layer of carbon dioxide covers the flame, because our breath has more oxygen than carbon dioxide.
Also, our breath does not extinguish the flame by cooling it as it is itself warmer than the coolness required to extinguish it.
So what is happening here?
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.


