Why must counterpoint be invertible when it accompanies a subject and countersubject?

In the context of a fugue, a countersubject is a contrapuntal voice that accompanies the subject throughout the piece. Because these two melodic lines are intended to recur together in different voices, the counterpoint must be invertible to ensure the musical relationship remains harmonious regardless of which part is positioned above or below the other.1

By utilizing invertible counterpoint, a composer ensures that the contrapuntal lines sound equally effective when their vertical order is rearranged. This technique allows for greater flexibility and complexity in the fugue's texture, as the subject and countersubject can be swapped between voices without violating the rules of harmonic consonance.12