I have a floppy disk cable where some wires are reversed. Why is this? Should I connect the drive to the side where no wires are reversed and the middle to the motherboard or the side where they are reversed?

The twisted end determines the drive designation.  The drive on the far end of the twist would be A and on the near end of the twist would be B.  The drive should be placed on the far end of the cable.  That sets it as the A drive, and places the drive's terminating resisters on the far end of the cable, where they are needed.

The twisted end determines the drive designation.  The drive on the far end of the twist would be A and on the near end of the twist would be B.  The drive should be placed on the far end of the cable.  That sets it as the A drive, and places the drive's terminating resisters on the far end of the cable, where they are needed.

Thank you!

Floppy disks, now that takes me back..! Don't use them these days, but I do still have a USB 3.5" drive in the desk drawer should I ever need it.

Originally there were "A/B" switches on the drive units (similarly as "master/slave" on IDE HDDs or CDROMs way later in time, but the floppy drives needed more than just a single jumper - often a cause of wrong, even inconsistent setting), but then the twisting cable trick came along. Consequently all drive makers get rid of the jumpers and permanently configure the drives as "B" and rely on the (then standard) twisting to remap it on the cable end to A... This got rid of the misconfiguration problems (if not all jumpers were set consistently to either A or B or some lost contact, the system did not work and all bios build in floppy diagnostic returned hard to debug nonsense).