I guess this is to avoid 'locallised' areas of cooling - e.g cooling faster at the surface where evapouration occurs - or faster cooling at the sides of the flask where you have contact to the ice bath - i.e. the liquid in the middle of the flask may end up slightly warmer (convection currents will average this out eventually, but not imeadiatley). If your measuring the exact freezing/melting point, then you want to make sure your reading is accurate and representitive of the whole body.
This might be an interesting (or at least informative) experiment:
do your cooling in a flask that is large enough. Clamp in 3 or 4 thermometers - one just below the surface, one in the middle of the sample, one right near the edge of the vessel and one right at the bottem. Don't stir and observe the readings on each thermometer as the sample cools to freezing from warm. You won't see that much of a difference, but there will be enough to confuse a freezing point expt. I would bet.