why can the combined weights of several liquids mixed in an open flask be less than but never more than the sum of all the weights of the ingredients?

Because you are never adding more than the substances created, nor are you creating any, but should a chemical reaction take place you could see the liquid change form into a gaseous state and that would result a loss of the liquid volume.
So to wrap it all up you can’t have more liquids than what is already there but you could always lose some due to a chemical change, hence the reason it says an open flask, the chemical change would not be collected, mass would be lost