Why does the harmonic minor scale contain an augmented second?

The harmonic minor scale contains an augmented second because of the specific way it is constructed to function within Western tonality.

A natural minor scale consists of a series of whole and half steps that result in a minor seventh interval from the tonic. In music theory, the seventh tone is often raised by a half step to create a "leading tone"—a note that is a half step below the tonic and provides a stronger sense of resolution to the key center.12

When you raise the seventh tone of a natural minor scale by a half step, you increase the distance between the sixth tone and the seventh tone. In many minor keys, the sixth tone is a half step lower than the sixth tone of the corresponding major scale. Raising the seventh tone while keeping the lowered sixth tone creates a gap of three semitones (a step and a half) between these two notes. Because this interval spans two scale degrees but is larger than a major second, it is classified as an augmented second.23