This is an apparent contradiction because blowing a flame has two counteracting effects. On the one hand, blowing brings more oxygen to the flame, which stimulates combustion. On the other hand, you also cool the flame, which makes combustion more difficult.
In the case of the candle flame, you blow the warm air away from the candle so that this heat is no longer in contact with the fuel (the melted wax in the wick). to restart the flame. With a candle with a thicker wick, there is more heat in the wick itself, which makes it more difficult to blow out a candle. Outdoor candles usually have very thick wicks so they don’t blow out easily. For the same reason, it is also more difficult to light an outdoor candle. It takes a while for the wax to melt and for the wick to heat up sufficiently.
With a campfire, all the wood is heated by the flames, which means that the heat capacity of the whole is much greater. The cooling by blowing is then negligible and you only see the stimulating effect of the extra oxygen.
prof. Dr. ir. Toon Verstraelen