Why does The Well-Tempered Clavier include pieces in every major and minor key?

The Well-Tempered Clavier was composed by Johann Sebastian Bach as a collection of 48 preludes and fugues designed to explore the intricacies of all 12 major and 12 minor keys.

The collection served two primary purposes:

• Pedagogical Instruction: The pieces were intended as exercises to provide keyboard players with practical experience in working with the chords, scales, and arpeggios associated with every key.
• Demonstrating Tuning Systems: The title refers to the use of a well-tempered tuning system, which allowed instruments to be played in all keys—a significant departure from the limitations of the meantone temperament common in Bach's era. By utilizing this system, Bach demonstrated that keyboard instruments could be played in any key without the need for constant, disruptive retuning, thereby expanding the harmonic possibilities available to composers and performers.12