What is the point of using molality when we have molarity?
One of the key attractions of molality is that changing the temperature of a solution does not change the molality, while it may change the molarity. This is because the volume of the solution changes as a result of expansion or contraction of the solvent upon changing the temperature, and thus the molarity changes, since $$M=\frac{n}{V}.$$

The downside, of course, is that the amount of solute required to reach a given molality depends on the nature of the solvent; ambiguity may also arise when a mixed solvent system (e.g. a water-ethanol mixture) is used, as the choice of which compound is the solute changes the molality of the resultant solution.1 Molarity avoids this problem by requiring only the volume of solvent.

As for why it's introduced in school, that's a pedagogical question beyond the scope of this answer, but both molarity and molality have their uses in the laboratory.



1 Consider, for example, a solvent made from 95% water and 5% ethanol. Molality could be determined with respect to only the water, or the combined water-ethanol solution, leading to different calculated concentrations.