We think of a fast Irish dance, with music in two triplet beats. The tradition in Bach’s era was to compose a jig as the last movement of a suite or, in this case, a partita. Bach may have composed it originally in 6, but decided there was more potential for rhythmic interest in duple meter.
If we expected a jig, we’re getting way more than we bargained for. The piece is written as two fugues, the subject of the first half inverted to create the theme for the second half. (The original, un-inverted form comes back just before the end of the second half, in stretto now against itself, or something reminiscent of itself.)
The theme feels angular and jagged. Why? It contains big leaps that simultaneously imply changes in harmony. If the theme leaps an octave, that’s not disturbing to the ear, but the it’s hard for us to hear a single melody when it modulates and jumps at the same time, and does this more than once. To our 20th century ears, it hangs together, but I wonder how Bach’s contemporaries might have heard it.
This is how he might have written it originally, reconstructed in 6: