Why does a candle flame go out when you blow on it?

Question

but a larger flame is kindled?

Answer 1

you are blowing carbon dioxide on the flame and the carbon dioxide makes it go out

Answer 2

It is a matter of size as you suggest.  The heat from the candle flame must turn liquid (melted) wax into a vapor that rises and burns.  Blowing on the candle drives the vapor away from the existing flame and adds cooler air in its place.  Blowing upon a larger flame (in a fireplace?) merely adds more air and oxygen to the fire with relatively  nil cooling effect.