Why is the aeolian mode the minor scale?
In Western music, scales are the different ways to divide an octave in order to select interesting notes, usually seven, referred to as degrees.
In such music, thirds and fifths intervals are designed to have overlapping harmonics. Major and minor scales harness this fact, they are built from 3 juxtaposed triads to maximize consonances.
Constructing C minor scale from minor triads C, F, G generates the same intervals than the Aeolian mode of C major. However a scale is not a mode.
Other common scales are not built from triads, but by tweaking the degrees of major and minor scales, e.g. to introduce a leading tone in harmonic minor scale.
In tonal systems fifths and thirds play a major role, to the point major and minor scales are generated using triads obtained from three notes separated by fifths.
E.g. C major scale is obtained by major triads C (the tonic) and two notes at 5th intervals:
We do the same to generate a minor scale, except we use minor triads. E.g. C minor:
Intervals of the natural minor scale are also these of the Aeolian mode of C major.
It seems to me that the Phrygian mode is more minor than the Aeolian scale and should be known, at least from technical terms, as the minor scale.
The Phrygian mode (1 2 2 2 1 2 2) of C major, with its minor second, is perceived as the "most minor" mode of C major, among the ones with a perfect fifth.
However Ionian, Aeolian, Phrygian, ... modes are not scales, they are modes of C major scale. For example, they have no tonic, this notion belongs to the scale. Aeolian mode of C major is not synonymous of A minor.
The scale is based on degrees with specific properties and a whole theory based on them, the tonal system.
A mode, in the modern sense, is a particular use of a scale. It happens Aeolian mode of C major scale has the same intervals than a minor scale and the same note sequence than A minor.
See this answer for the differences between scale and mode.